x^2-5x+x+40=180

Solution for x^2-5x+x+40=180 equation:

x^2-5x+x+40=180

We move all terms to the left:

x^2-5x+x+40-(180)=0

We add all the numbers together, and all the variables

x^2-4x-140=0

a = 1; b = -4; c = -140;
Δ = b2-4ac
Δ = -42-4·1·(-140)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-24}{2*1}=\frac{-20}{2}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+24}{2*1}=\frac{28}{2}
=14
$