5x^2-2x+60=180

Solution for 5x^2-2x+60=180 equation:

5x^2-2x+60=180

We move all terms to the left:

5x^2-2x+60-(180)=0

We add all the numbers together, and all the variables

5x^2-2x-120=0

a = 5; b = -2; c = -120;
Δ = b2-4ac
Δ = -22-4·5·(-120)
Δ = 2404
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:

$\sqrt{\Delta}=\sqrt{2404}=\sqrt{4*601}=\sqrt{4}*\sqrt{601}=2\sqrt{601}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{601}}{2*5}=\frac{2-2\sqrt{601}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{601}}{2*5}=\frac{2+2\sqrt{601}}{10}
$