60x^2-40x=175

Solution for 60x^2-40x=175 equation:

60x^2-40x=175

We move all terms to the left:

60x^2-40x-(175)=0

a = 60; b = -40; c = -175;
Δ = b2-4ac
Δ = -402-4·60·(-175)
Δ = 43600
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:

$\sqrt{\Delta}=\sqrt{43600}=\sqrt{400*109}=\sqrt{400}*\sqrt{109}=20\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-20\sqrt{109}}{2*60}=\frac{40-20\sqrt{109}}{120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+20\sqrt{109}}{2*60}=\frac{40+20\sqrt{109}}{120}
$