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4x(4x-1)=2112
We move all terms to the left:
4x(4x-1)-(2112)=0
We multiply parentheses
16x^2-4x-2112=0
a = 16; b = -4; c = -2112;
Δ = b2-4ac
Δ = -42-4·16·(-2112)
Δ = 135184
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{135184}=\sqrt{16*8449}=\sqrt{16}*\sqrt{8449}=4\sqrt{8449}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{8449}}{2*16}=\frac{4-4\sqrt{8449}}{32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{8449}}{2*16}=\frac{4+4\sqrt{8449}}{32} $
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