(57+x)(x+87)+50=180

Solution for (57+x)(x+87)+50=180 equation:

(57+x)(x+87)+50=180

We move all terms to the left:

(57+x)(x+87)+50-(180)=0

We add all the numbers together, and all the variables

(x+57)(x+87)+50-180=0

We add all the numbers together, and all the variables

(x+57)(x+87)-130=0

We multiply parentheses ..

(+x^2+87x+57x+4959)-130=0

We get rid of parentheses

x^2+87x+57x+4959-130=0

We add all the numbers together, and all the variables

x^2+144x+4829=0

a = 1; b = 144; c = +4829;
Δ = b2-4ac
Δ = 1442-4·1·4829
Δ = 1420
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:

$\sqrt{\Delta}=\sqrt{1420}=\sqrt{4*355}=\sqrt{4}*\sqrt{355}=2\sqrt{355}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-2\sqrt{355}}{2*1}=\frac{-144-2\sqrt{355}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+2\sqrt{355}}{2*1}=\frac{-144+2\sqrt{355}}{2}
$