x^2+4x+5+75=180

Solution for x^2+4x+5+75=180 equation:

x^2+4x+5+75=180

We move all terms to the left:

x^2+4x+5+75-(180)=0

We add all the numbers together, and all the variables

x^2+4x-100=0

a = 1; b = 4; c = -100;
Δ = b2-4ac
Δ = 42-4·1·(-100)
Δ = 416
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:

$\sqrt{\Delta}=\sqrt{416}=\sqrt{16*26}=\sqrt{16}*\sqrt{26}=4\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{26}}{2*1}=\frac{-4-4\sqrt{26}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{26}}{2*1}=\frac{-4+4\sqrt{26}}{2}
$