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4x(x-5)=31
We move all terms to the left:
4x(x-5)-(31)=0
We multiply parentheses
4x^2-20x-31=0
a = 4; b = -20; c = -31;
Δ = b2-4ac
Δ = -202-4·4·(-31)
Δ = 896
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{896}=\sqrt{64*14}=\sqrt{64}*\sqrt{14}=8\sqrt{14}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-8\sqrt{14}}{2*4}=\frac{20-8\sqrt{14}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+8\sqrt{14}}{2*4}=\frac{20+8\sqrt{14}}{8} $
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