5x(x+54)+90=180

Solution for 5x(x+54)+90=180 equation:

5x(x+54)+90=180

We move all terms to the left:

5x(x+54)+90-(180)=0

We add all the numbers together, and all the variables

5x(x+54)-90=0

We multiply parentheses

5x^2+270x-90=0

a = 5; b = 270; c = -90;
Δ = b2-4ac
Δ = 2702-4·5·(-90)
Δ = 74700
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:

$\sqrt{\Delta}=\sqrt{74700}=\sqrt{900*83}=\sqrt{900}*\sqrt{83}=30\sqrt{83}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(270)-30\sqrt{83}}{2*5}=\frac{-270-30\sqrt{83}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(270)+30\sqrt{83}}{2*5}=\frac{-270+30\sqrt{83}}{10}
$