x+4x(x+45)=180

Solution for x+4x(x+45)=180 equation:

x+4x(x+45)=180

We move all terms to the left:

x+4x(x+45)-(180)=0

We multiply parentheses

4x^2+x+180x-180=0

We add all the numbers together, and all the variables

4x^2+181x-180=0

a = 4; b = 181; c = -180;
Δ = b2-4ac
Δ = 1812-4·4·(-180)
Δ = 35641
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(181)-\sqrt{35641}}{2*4}=\frac{-181-\sqrt{35641}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(181)+\sqrt{35641}}{2*4}=\frac{-181+\sqrt{35641}}{8}
$