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16x(5x+10)+96=540
We move all terms to the left:
16x(5x+10)+96-(540)=0
We add all the numbers together, and all the variables
16x(5x+10)-444=0
We multiply parentheses
80x^2+160x-444=0
a = 80; b = 160; c = -444;
Δ = b2-4ac
Δ = 1602-4·80·(-444)
Δ = 167680
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{167680}=\sqrt{256*655}=\sqrt{256}*\sqrt{655}=16\sqrt{655}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-16\sqrt{655}}{2*80}=\frac{-160-16\sqrt{655}}{160} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+16\sqrt{655}}{2*80}=\frac{-160+16\sqrt{655}}{160} $
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