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4x(x-1)=14
We move all terms to the left:
4x(x-1)-(14)=0
We multiply parentheses
4x^2-4x-14=0
a = 4; b = -4; c = -14;
Δ = b2-4ac
Δ = -42-4·4·(-14)
Δ = 240
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{15}}{2*4}=\frac{4-4\sqrt{15}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{15}}{2*4}=\frac{4+4\sqrt{15}}{8} $
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