4x+x^2+5x=180

Solution for 4x+x^2+5x=180 equation:

4x+x^2+5x=180

We move all terms to the left:

4x+x^2+5x-(180)=0

We add all the numbers together, and all the variables

x^2+9x-180=0

a = 1; b = 9; c = -180;
Δ = b2-4ac
Δ = 92-4·1·(-180)
Δ = 801
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:

$\sqrt{\Delta}=\sqrt{801}=\sqrt{9*89}=\sqrt{9}*\sqrt{89}=3\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{89}}{2*1}=\frac{-9-3\sqrt{89}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{89}}{2*1}=\frac{-9+3\sqrt{89}}{2}
$