12x^2+4x=172

Solution for 12x^2+4x=172 equation:

12x^2+4x=172

We move all terms to the left:

12x^2+4x-(172)=0

a = 12; b = 4; c = -172;
Δ = b2-4ac
Δ = 42-4·12·(-172)
Δ = 8272
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:

$\sqrt{\Delta}=\sqrt{8272}=\sqrt{16*517}=\sqrt{16}*\sqrt{517}=4\sqrt{517}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{517}}{2*12}=\frac{-4-4\sqrt{517}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{517}}{2*12}=\frac{-4+4\sqrt{517}}{24}
$