60x^2-20x=185

Solution for 60x^2-20x=185 equation:

60x^2-20x=185

We move all terms to the left:

60x^2-20x-(185)=0

a = 60; b = -20; c = -185;
Δ = b2-4ac
Δ = -202-4·60·(-185)
Δ = 44800
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:

$\sqrt{\Delta}=\sqrt{44800}=\sqrt{6400*7}=\sqrt{6400}*\sqrt{7}=80\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-80\sqrt{7}}{2*60}=\frac{20-80\sqrt{7}}{120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+80\sqrt{7}}{2*60}=\frac{20+80\sqrt{7}}{120}
$