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3x-12+3x=3x^2-9x
We move all terms to the left:
3x-12+3x-(3x^2-9x)=0
We add all the numbers together, and all the variables
6x-(3x^2-9x)-12=0
We get rid of parentheses
-3x^2+6x+9x-12=0
We add all the numbers together, and all the variables
-3x^2+15x-12=0
a = -3; b = 15; c = -12;
Δ = b2-4ac
Δ = 152-4·(-3)·(-12)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{81}=9$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-9}{2*-3}=\frac{-24}{-6} =+4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+9}{2*-3}=\frac{-6}{-6} =1 $
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