12x^2-32x=-19

Solution for 12x^2-32x=-19 equation:

12x^2-32x=-19

We move all terms to the left:

12x^2-32x-(-19)=0

We add all the numbers together, and all the variables

12x^2-32x+19=0

a = 12; b = -32; c = +19;
Δ = b2-4ac
Δ = -322-4·12·19
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{7}}{2*12}=\frac{32-4\sqrt{7}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{7}}{2*12}=\frac{32+4\sqrt{7}}{24}
$