2x2+32x=12

Solution for 2x2+32x=12 equation:

2x^2+32x=12

We move all terms to the left:

2x^2+32x-(12)=0

a = 2; b = 32; c = -12;
Δ = b2-4ac
Δ = 322-4·2·(-12)
Δ = 1120
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:

$\sqrt{\Delta}=\sqrt{1120}=\sqrt{16*70}=\sqrt{16}*\sqrt{70}=4\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{70}}{2*2}=\frac{-32-4\sqrt{70}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{70}}{2*2}=\frac{-32+4\sqrt{70}}{4}
$