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(2x+7)(9x-33)=118
We move all terms to the left:
(2x+7)(9x-33)-(118)=0
We multiply parentheses ..
(+18x^2-66x+63x-231)-118=0
We get rid of parentheses
18x^2-66x+63x-231-118=0
We add all the numbers together, and all the variables
18x^2-3x-349=0
a = 18; b = -3; c = -349;
Δ = b2-4ac
Δ = -32-4·18·(-349)
Δ = 25137
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{25137}=\sqrt{441*57}=\sqrt{441}*\sqrt{57}=21\sqrt{57}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-21\sqrt{57}}{2*18}=\frac{3-21\sqrt{57}}{36} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+21\sqrt{57}}{2*18}=\frac{3+21\sqrt{57}}{36} $
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