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(5x+3)(4x-8)=180
We move all terms to the left:
(5x+3)(4x-8)-(180)=0
We multiply parentheses ..
(+20x^2-40x+12x-24)-180=0
We get rid of parentheses
20x^2-40x+12x-24-180=0
We add all the numbers together, and all the variables
20x^2-28x-204=0
a = 20; b = -28; c = -204;
Δ = b2-4ac
Δ = -282-4·20·(-204)
Δ = 17104
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{17104}=\sqrt{16*1069}=\sqrt{16}*\sqrt{1069}=4\sqrt{1069}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{1069}}{2*20}=\frac{28-4\sqrt{1069}}{40} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{1069}}{2*20}=\frac{28+4\sqrt{1069}}{40} $
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