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

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

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

We move all terms to the left:

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

We multiply parentheses

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

We add all the numbers together, and all the variables

2X^2+45X-180=0

a = 2; b = 45; c = -180;
Δ = b2-4ac
Δ = 452-4·2·(-180)
Δ = 3465
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:

$\sqrt{\Delta}=\sqrt{3465}=\sqrt{9*385}=\sqrt{9}*\sqrt{385}=3\sqrt{385}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-3\sqrt{385}}{2*2}=\frac{-45-3\sqrt{385}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+3\sqrt{385}}{2*2}=\frac{-45+3\sqrt{385}}{4}
$