5x(17x-18)=180

Solution for 5x(17x-18)=180 equation:

5x(17x-18)=180

We move all terms to the left:

5x(17x-18)-(180)=0

We multiply parentheses

85x^2-90x-180=0

a = 85; b = -90; c = -180;
Δ = b2-4ac
Δ = -902-4·85·(-180)
Δ = 69300
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:

$\sqrt{\Delta}=\sqrt{69300}=\sqrt{900*77}=\sqrt{900}*\sqrt{77}=30\sqrt{77}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-30\sqrt{77}}{2*85}=\frac{90-30\sqrt{77}}{170}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+30\sqrt{77}}{2*85}=\frac{90+30\sqrt{77}}{170}
$