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4x(2x-1)=16
We move all terms to the left:
4x(2x-1)-(16)=0
We multiply parentheses
8x^2-4x-16=0
a = 8; b = -4; c = -16;
Δ = b2-4ac
Δ = -42-4·8·(-16)
Δ = 528
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{33}}{2*8}=\frac{4-4\sqrt{33}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{33}}{2*8}=\frac{4+4\sqrt{33}}{16} $
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