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5x(4x-1)=80
We move all terms to the left:
5x(4x-1)-(80)=0
We multiply parentheses
20x^2-5x-80=0
a = 20; b = -5; c = -80;
Δ = b2-4ac
Δ = -52-4·20·(-80)
Δ = 6425
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6425}=\sqrt{25*257}=\sqrt{25}*\sqrt{257}=5\sqrt{257}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{257}}{2*20}=\frac{5-5\sqrt{257}}{40} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{257}}{2*20}=\frac{5+5\sqrt{257}}{40} $
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