100x+200x*x=0

Solution for 100x+200x*x=0 equation:

100x+200x*x=0

Wy multiply elements

200x^2+100x=0

a = 200; b = 100; c = 0;
Δ = b2-4ac
Δ = 1002-4·200·0
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-100}{2*200}=\frac{-200}{400}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+100}{2*200}=\frac{0}{400}
=0
$