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(4x+45)(5x-18)=180
We move all terms to the left:
(4x+45)(5x-18)-(180)=0
We multiply parentheses ..
(+20x^2-72x+225x-810)-180=0
We get rid of parentheses
20x^2-72x+225x-810-180=0
We add all the numbers together, and all the variables
20x^2+153x-990=0
a = 20; b = 153; c = -990;
Δ = b2-4ac
Δ = 1532-4·20·(-990)
Δ = 102609
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{102609}=\sqrt{9*11401}=\sqrt{9}*\sqrt{11401}=3\sqrt{11401}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(153)-3\sqrt{11401}}{2*20}=\frac{-153-3\sqrt{11401}}{40} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(153)+3\sqrt{11401}}{2*20}=\frac{-153+3\sqrt{11401}}{40} $
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