600-x*x=x*x+50x

Solution for 600-x*x=x*x+50x equation:

600-x*x=x*x+50x

We move all terms to the left:

600-x*x-(x*x+50x)=0

We add all the numbers together, and all the variables

-x*x-(+50x+x*x)+600=0

Wy multiply elements

-1x^2-(+50x+x*x)+600=0

We get rid of parentheses

-1x^2-50x-x*x+600=0

Wy multiply elements

-1x^2-1x^2-50x+600=0

We add all the numbers together, and all the variables

-2x^2-50x+600=0

a = -2; b = -50; c = +600;
Δ = b2-4ac
Δ = -502-4·(-2)·600
Δ = 7300
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:

$\sqrt{\Delta}=\sqrt{7300}=\sqrt{100*73}=\sqrt{100}*\sqrt{73}=10\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-10\sqrt{73}}{2*-2}=\frac{50-10\sqrt{73}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+10\sqrt{73}}{2*-2}=\frac{50+10\sqrt{73}}{-4}
$