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4x(x-5)=80
We move all terms to the left:
4x(x-5)-(80)=0
We multiply parentheses
4x^2-20x-80=0
a = 4; b = -20; c = -80;
Δ = b2-4ac
Δ = -202-4·4·(-80)
Δ = 1680
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1680}=\sqrt{16*105}=\sqrt{16}*\sqrt{105}=4\sqrt{105}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{105}}{2*4}=\frac{20-4\sqrt{105}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{105}}{2*4}=\frac{20+4\sqrt{105}}{8} $
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