12x^2+800x=920

Solution for 12x^2+800x=920 equation:

12x^2+800x=920

We move all terms to the left:

12x^2+800x-(920)=0

a = 12; b = 800; c = -920;
Δ = b2-4ac
Δ = 8002-4·12·(-920)
Δ = 684160
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:

$\sqrt{\Delta}=\sqrt{684160}=\sqrt{64*10690}=\sqrt{64}*\sqrt{10690}=8\sqrt{10690}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(800)-8\sqrt{10690}}{2*12}=\frac{-800-8\sqrt{10690}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(800)+8\sqrt{10690}}{2*12}=\frac{-800+8\sqrt{10690}}{24}
$