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8x(6x+20)=180
We move all terms to the left:
8x(6x+20)-(180)=0
We multiply parentheses
48x^2+160x-180=0
a = 48; b = 160; c = -180;
Δ = b2-4ac
Δ = 1602-4·48·(-180)
Δ = 60160
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{60160}=\sqrt{256*235}=\sqrt{256}*\sqrt{235}=16\sqrt{235}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-16\sqrt{235}}{2*48}=\frac{-160-16\sqrt{235}}{96} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+16\sqrt{235}}{2*48}=\frac{-160+16\sqrt{235}}{96} $
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