X^2+100x=5000

Solution for X^2+100x=5000 equation:

X^2+100X=5000

We move all terms to the left:

X^2+100X-(5000)=0

a = 1; b = 100; c = -5000;
Δ = b2-4ac
Δ = 1002-4·1·(-5000)
Δ = 30000
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:

$\sqrt{\Delta}=\sqrt{30000}=\sqrt{10000*3}=\sqrt{10000}*\sqrt{3}=100\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-100\sqrt{3}}{2*1}=\frac{-100-100\sqrt{3}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+100\sqrt{3}}{2*1}=\frac{-100+100\sqrt{3}}{2}
$