4x(4x+1)=2112

Solution for 4x(4x+1)=2112 equation:

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}
$