12x^2-24x-40=40

Solution for 12x^2-24x-40=40 equation:

12x^2-24x-40=40

We move all terms to the left:

12x^2-24x-40-(40)=0

We add all the numbers together, and all the variables

12x^2-24x-80=0

a = 12; b = -24; c = -80;
Δ = b2-4ac
Δ = -242-4·12·(-80)
Δ = 4416
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:

$\sqrt{\Delta}=\sqrt{4416}=\sqrt{64*69}=\sqrt{64}*\sqrt{69}=8\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{69}}{2*12}=\frac{24-8\sqrt{69}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{69}}{2*12}=\frac{24+8\sqrt{69}}{24}
$