X^2+X^2+20x+100x=2500

Solution for X^2+X^2+20x+100x=2500 equation:

X^2+X^2+20X+100X=2500

We move all terms to the left:

X^2+X^2+20X+100X-(2500)=0

We add all the numbers together, and all the variables

2X^2+120X-2500=0

a = 2; b = 120; c = -2500;
Δ = b2-4ac
Δ = 1202-4·2·(-2500)
Δ = 34400
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:

$\sqrt{\Delta}=\sqrt{34400}=\sqrt{400*86}=\sqrt{400}*\sqrt{86}=20\sqrt{86}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-20\sqrt{86}}{2*2}=\frac{-120-20\sqrt{86}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+20\sqrt{86}}{2*2}=\frac{-120+20\sqrt{86}}{4}
$