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(2x-6)(3x-6)=18
We move all terms to the left:
(2x-6)(3x-6)-(18)=0
We multiply parentheses ..
(+6x^2-12x-18x+36)-18=0
We get rid of parentheses
6x^2-12x-18x+36-18=0
We add all the numbers together, and all the variables
6x^2-30x+18=0
a = 6; b = -30; c = +18;
Δ = b2-4ac
Δ = -302-4·6·18
Δ = 468
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{13}}{2*6}=\frac{30-6\sqrt{13}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{13}}{2*6}=\frac{30+6\sqrt{13}}{12} $
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