4x^2-80x=60

Solution for 4x^2-80x=60 equation:

4x^2-80x=60

We move all terms to the left:

4x^2-80x-(60)=0

a = 4; b = -80; c = -60;
Δ = b2-4ac
Δ = -802-4·4·(-60)
Δ = 7360
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:

$\sqrt{\Delta}=\sqrt{7360}=\sqrt{64*115}=\sqrt{64}*\sqrt{115}=8\sqrt{115}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-8\sqrt{115}}{2*4}=\frac{80-8\sqrt{115}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+8\sqrt{115}}{2*4}=\frac{80+8\sqrt{115}}{8}
$