(6x+6)(3x-15)=180

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Solution for (6x+6)(3x-15)=180 equation:



(6x+6)(3x-15)=180
We move all terms to the left:
(6x+6)(3x-15)-(180)=0
We multiply parentheses ..
(+18x^2-90x+18x-90)-180=0
We get rid of parentheses
18x^2-90x+18x-90-180=0
We add all the numbers together, and all the variables
18x^2-72x-270=0
a = 18; b = -72; c = -270;
Δ = b2-4ac
Δ = -722-4·18·(-270)
Δ = 24624
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:
$\sqrt{\Delta}=\sqrt{24624}=\sqrt{1296*19}=\sqrt{1296}*\sqrt{19}=36\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-36\sqrt{19}}{2*18}=\frac{72-36\sqrt{19}}{36} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+36\sqrt{19}}{2*18}=\frac{72+36\sqrt{19}}{36} $

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