(X-10)(x+55)=180

Solution for (X-10)(x+55)=180 equation:

(X-10)(X+55)=180

We move all terms to the left:

(X-10)(X+55)-(180)=0

We multiply parentheses ..

(+X^2+55X-10X-550)-180=0

We get rid of parentheses

X^2+55X-10X-550-180=0

We add all the numbers together, and all the variables

X^2+45X-730=0

a = 1; b = 45; c = -730;
Δ = b2-4ac
Δ = 452-4·1·(-730)
Δ = 4945
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{-(45)-\sqrt{4945}}{2*1}=\frac{-45-\sqrt{4945}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{4945}}{2*1}=\frac{-45+\sqrt{4945}}{2}
$