(X+4)(x-5)+x=180

Solution for (X+4)(x-5)+x=180 equation:

(X+4)(X-5)+X=180

We move all terms to the left:

(X+4)(X-5)+X-(180)=0

We add all the numbers together, and all the variables

X+(X+4)(X-5)-180=0

We multiply parentheses ..

(+X^2-5X+4X-20)+X-180=0

We get rid of parentheses

X^2-5X+4X+X-20-180=0

We add all the numbers together, and all the variables

X^2-200=0

a = 1; b = 0; c = -200;
Δ = b2-4ac
Δ = 02-4·1·(-200)
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{2}}{2*1}=\frac{0-20\sqrt{2}}{2}
=-\frac{20\sqrt{2}}{2}
=-10\sqrt{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{2}}{2*1}=\frac{0+20\sqrt{2}}{2}
=\frac{20\sqrt{2}}{2}
=10\sqrt{2}
$