(x-18)5x=180

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

(x-18)5x=180

We move all terms to the left:

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

We multiply parentheses

5x^2-90x-180=0

a = 5; b = -90; c = -180;
Δ = b2-4ac
Δ = -902-4·5·(-180)
Δ = 11700
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:

$\sqrt{\Delta}=\sqrt{11700}=\sqrt{900*13}=\sqrt{900}*\sqrt{13}=30\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-30\sqrt{13}}{2*5}=\frac{90-30\sqrt{13}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+30\sqrt{13}}{2*5}=\frac{90+30\sqrt{13}}{10}
$