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(x+93)(x+55)=180
We move all terms to the left:
(x+93)(x+55)-(180)=0
We multiply parentheses ..
(+x^2+55x+93x+5115)-180=0
We get rid of parentheses
x^2+55x+93x+5115-180=0
We add all the numbers together, and all the variables
x^2+148x+4935=0
a = 1; b = 148; c = +4935;
Δ = b2-4ac
Δ = 1482-4·1·4935
Δ = 2164
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2164}=\sqrt{4*541}=\sqrt{4}*\sqrt{541}=2\sqrt{541}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(148)-2\sqrt{541}}{2*1}=\frac{-148-2\sqrt{541}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(148)+2\sqrt{541}}{2*1}=\frac{-148+2\sqrt{541}}{2} $
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