5x^2-3x=180

Solution for 5x^2-3x=180 equation:

5x^2-3x=180

We move all terms to the left:

5x^2-3x-(180)=0

a = 5; b = -3; c = -180;
Δ = b2-4ac
Δ = -32-4·5·(-180)
Δ = 3609
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:

$\sqrt{\Delta}=\sqrt{3609}=\sqrt{9*401}=\sqrt{9}*\sqrt{401}=3\sqrt{401}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{401}}{2*5}=\frac{3-3\sqrt{401}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{401}}{2*5}=\frac{3+3\sqrt{401}}{10}
$