100x^2+100x=200

Solution for 100x^2+100x=200 equation:

100x^2+100x=200

We move all terms to the left:

100x^2+100x-(200)=0

a = 100; b = 100; c = -200;
Δ = b2-4ac
Δ = 1002-4·100·(-200)
Δ = 90000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{90000}=300$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-300}{2*100}=\frac{-400}{200}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+300}{2*100}=\frac{200}{200}
=1
$