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(x+23)(5x-9)=180
We move all terms to the left:
(x+23)(5x-9)-(180)=0
We multiply parentheses ..
(+5x^2-9x+115x-207)-180=0
We get rid of parentheses
5x^2-9x+115x-207-180=0
We add all the numbers together, and all the variables
5x^2+106x-387=0
a = 5; b = 106; c = -387;
Δ = b2-4ac
Δ = 1062-4·5·(-387)
Δ = 18976
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{18976}=\sqrt{16*1186}=\sqrt{16}*\sqrt{1186}=4\sqrt{1186}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(106)-4\sqrt{1186}}{2*5}=\frac{-106-4\sqrt{1186}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(106)+4\sqrt{1186}}{2*5}=\frac{-106+4\sqrt{1186}}{10} $
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