5x^2-4x=60

Solution for 5x^2-4x=60 equation:

5x^2-4x=60

We move all terms to the left:

5x^2-4x-(60)=0

a = 5; b = -4; c = -60;
Δ = b2-4ac
Δ = -42-4·5·(-60)
Δ = 1216
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:

$\sqrt{\Delta}=\sqrt{1216}=\sqrt{64*19}=\sqrt{64}*\sqrt{19}=8\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8\sqrt{19}}{2*5}=\frac{4-8\sqrt{19}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8\sqrt{19}}{2*5}=\frac{4+8\sqrt{19}}{10}
$