12x^2-68x=-96

Solution for 12x^2-68x=-96 equation:

12x^2-68x=-96

We move all terms to the left:

12x^2-68x-(-96)=0

We add all the numbers together, and all the variables

12x^2-68x+96=0

a = 12; b = -68; c = +96;
Δ = b2-4ac
Δ = -682-4·12·96
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-4}{2*12}=\frac{64}{24}
=2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+4}{2*12}=\frac{72}{24}
=3
$