96x^2-12x=112

Solution for 96x^2-12x=112 equation:

96x^2-12x=112

We move all terms to the left:

96x^2-12x-(112)=0

a = 96; b = -12; c = -112;
Δ = b2-4ac
Δ = -122-4·96·(-112)
Δ = 43152
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:

$\sqrt{\Delta}=\sqrt{43152}=\sqrt{16*2697}=\sqrt{16}*\sqrt{2697}=4\sqrt{2697}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{2697}}{2*96}=\frac{12-4\sqrt{2697}}{192}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{2697}}{2*96}=\frac{12+4\sqrt{2697}}{192}
$