45+x(2x+15)=180

Solution for 45+x(2x+15)=180 equation:

45+x(2x+15)=180

We move all terms to the left:

45+x(2x+15)-(180)=0

We add all the numbers together, and all the variables

x(2x+15)-135=0

We multiply parentheses

2x^2+15x-135=0

a = 2; b = 15; c = -135;
Δ = b2-4ac
Δ = 152-4·2·(-135)
Δ = 1305
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:

$\sqrt{\Delta}=\sqrt{1305}=\sqrt{9*145}=\sqrt{9}*\sqrt{145}=3\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{145}}{2*2}=\frac{-15-3\sqrt{145}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{145}}{2*2}=\frac{-15+3\sqrt{145}}{4}
$