25x^2-12x=320

Solution for 25x^2-12x=320 equation:

25x^2-12x=320

We move all terms to the left:

25x^2-12x-(320)=0

a = 25; b = -12; c = -320;
Δ = b2-4ac
Δ = -122-4·25·(-320)
Δ = 32144
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:

$\sqrt{\Delta}=\sqrt{32144}=\sqrt{784*41}=\sqrt{784}*\sqrt{41}=28\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-28\sqrt{41}}{2*25}=\frac{12-28\sqrt{41}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+28\sqrt{41}}{2*25}=\frac{12+28\sqrt{41}}{50}
$