2x(5x-23)=180

Solution for 2x(5x-23)=180 equation:

2x(5x-23)=180

We move all terms to the left:

2x(5x-23)-(180)=0

We multiply parentheses

10x^2-46x-180=0

a = 10; b = -46; c = -180;
Δ = b2-4ac
Δ = -462-4·10·(-180)
Δ = 9316
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:

$\sqrt{\Delta}=\sqrt{9316}=\sqrt{4*2329}=\sqrt{4}*\sqrt{2329}=2\sqrt{2329}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-2\sqrt{2329}}{2*10}=\frac{46-2\sqrt{2329}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+2\sqrt{2329}}{2*10}=\frac{46+2\sqrt{2329}}{20}
$