If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

# Worked example: quadratic formula (negative coefficients)

Sal solves -3x^2+10x-3=0 by plugging a=-3, b=10, c=-3 in the quadratic formula. Then he multiplies everything by -1 and solves again. The results are the same! Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• What do I do if the number inside the square root is not a perfect square? For example: 10x^2 -9x -6 = 0
• You have to see if there are any perfect square factors of the number that can be taken out. So b^2 - 4ac = (-9)^2 - 4(10)(-6) = 81 + 240 = 321. I can divide by three to get 3*107, but there are no other factors, so all you can do is leave it as √321, so the answers will be x = (9 ± √321)/20.
• how do you remember the formula? I keep forgetting.
• The more you say it, write it, and hear it, the quicker it will get into short term and long term memory, so keep doing all three of these things. I hate it when my students do not want to say things out loud because they think it is silly, but it works. Practice with trying to tell your mom or dad, they may remember it from when they were in high school.
• Where did he get the second equation from?
• When we have a quadratic equation or expression, does it matter to which side we minus or subtract the terms to match ax squared + bx + c?
Do we have to pull the terms to the left side?
• What does Sal mean by "the roots of this equation?" I just think of it being the solutions of the equation.
• "Roots" of an equation means the values of x that satisfy the equation ax^2 + bx + c = 0. So yes it's more like the solution to the quadratic equation.
• my dad dosent love me anyone because i dont understand quadratics
• just learn it
• Yes, it works for all quadratic equations. You just need to simplify the quadratic and write it in the form: Ax^2 + Bx + C = 0 before using the formula.
• When you start with a negative b like in the equation -6x^2 -3x +6 and you are trying to insert it in the equation with the a, b, and c's do you keep -3 or change it to 3 for the first -b?
Sry if it doesn't make sense
• In the quadratic formula, it’s -b, so when you plug in, you would do -(-3) which is same thing as +3.