600(50+x)-600(50-x)=2500-x2

Solution for 600(50+x)-600(50-x)=2500-x2 equation:

600(50+x)-600(50-x)=2500-x2

We move all terms to the left:

600(50+x)-600(50-x)-(2500-x2)=0

We add all the numbers together, and all the variables

-(-1x^2+2500)+600(x+50)-600(-1x+50)=0

We multiply parentheses

-(-1x^2+2500)+600x+600x+30000-30000=0

We get rid of parentheses

1x^2+600x+600x-2500+30000-30000=0

We add all the numbers together, and all the variables

x^2+1200x-2500=0

a = 1; b = 1200; c = -2500;
Δ = b2-4ac
Δ = 12002-4·1·(-2500)
Δ = 1450000
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:

$\sqrt{\Delta}=\sqrt{1450000}=\sqrt{10000*145}=\sqrt{10000}*\sqrt{145}=100\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1200)-100\sqrt{145}}{2*1}=\frac{-1200-100\sqrt{145}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1200)+100\sqrt{145}}{2*1}=\frac{-1200+100\sqrt{145}}{2}
$