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4x(x-1)=31
We move all terms to the left:
4x(x-1)-(31)=0
We multiply parentheses
4x^2-4x-31=0
a = 4; b = -4; c = -31;
Δ = b2-4ac
Δ = -42-4·4·(-31)
Δ = 512
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{512}=\sqrt{256*2}=\sqrt{256}*\sqrt{2}=16\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-16\sqrt{2}}{2*4}=\frac{4-16\sqrt{2}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+16\sqrt{2}}{2*4}=\frac{4+16\sqrt{2}}{8} $
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