(180-x*x)+(150-2x)=180

Solution for (180-x*x)+(150-2x)=180 equation:

(180-x*x)+(150-2x)=180

We move all terms to the left:

(180-x*x)+(150-2x)-(180)=0

We add all the numbers together, and all the variables

(-x*x+180)+(-2x+150)-180=0

We get rid of parentheses

-x*x-2x+180+150-180=0

We add all the numbers together, and all the variables

-2x-x*x+150=0

Wy multiply elements

-1x^2-2x+150=0

a = -1; b = -2; c = +150;
Δ = b2-4ac
Δ = -22-4·(-1)·150
Δ = 604
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:

$\sqrt{\Delta}=\sqrt{604}=\sqrt{4*151}=\sqrt{4}*\sqrt{151}=2\sqrt{151}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{151}}{2*-1}=\frac{2-2\sqrt{151}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{151}}{2*-1}=\frac{2+2\sqrt{151}}{-2}
$