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(5x-8)(3x-32)=180
We move all terms to the left:
(5x-8)(3x-32)-(180)=0
We multiply parentheses ..
(+15x^2-160x-24x+256)-180=0
We get rid of parentheses
15x^2-160x-24x+256-180=0
We add all the numbers together, and all the variables
15x^2-184x+76=0
a = 15; b = -184; c = +76;
Δ = b2-4ac
Δ = -1842-4·15·76
Δ = 29296
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{29296}=\sqrt{16*1831}=\sqrt{16}*\sqrt{1831}=4\sqrt{1831}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-184)-4\sqrt{1831}}{2*15}=\frac{184-4\sqrt{1831}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-184)+4\sqrt{1831}}{2*15}=\frac{184+4\sqrt{1831}}{30} $
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