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(6x+6)(5x-24)=180
We move all terms to the left:
(6x+6)(5x-24)-(180)=0
We multiply parentheses ..
(+30x^2-144x+30x-144)-180=0
We get rid of parentheses
30x^2-144x+30x-144-180=0
We add all the numbers together, and all the variables
30x^2-114x-324=0
a = 30; b = -114; c = -324;
Δ = b2-4ac
Δ = -1142-4·30·(-324)
Δ = 51876
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{51876}=\sqrt{36*1441}=\sqrt{36}*\sqrt{1441}=6\sqrt{1441}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-114)-6\sqrt{1441}}{2*30}=\frac{114-6\sqrt{1441}}{60} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-114)+6\sqrt{1441}}{2*30}=\frac{114+6\sqrt{1441}}{60} $
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