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6x+6(x-9)=x^2-9x
We move all terms to the left:
6x+6(x-9)-(x^2-9x)=0
We multiply parentheses
6x+6x-(x^2-9x)-54=0
We get rid of parentheses
-x^2+6x+6x+9x-54=0
We add all the numbers together, and all the variables
-1x^2+21x-54=0
a = -1; b = 21; c = -54;
Δ = b2-4ac
Δ = 212-4·(-1)·(-54)
Δ = 225
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{225}=15$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-15}{2*-1}=\frac{-36}{-2} =+18 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+15}{2*-1}=\frac{-6}{-2} =+3 $
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