12x^2-68x=-40

Solution for 12x^2-68x=-40 equation:

12x^2-68x=-40

We move all terms to the left:

12x^2-68x-(-40)=0

We add all the numbers together, and all the variables

12x^2-68x+40=0

a = 12; b = -68; c = +40;
Δ = b2-4ac
Δ = -682-4·12·40
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-52}{2*12}=\frac{16}{24}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+52}{2*12}=\frac{120}{24}
=5
$