200X^2+100x-2=0

Solution for 200X^2+100x-2=0 equation:

200X^2+100X-2=0

a = 200; b = 100; c = -2;
Δ = b2-4ac
Δ = 1002-4·200·(-2)
Δ = 11600
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:

$\sqrt{\Delta}=\sqrt{11600}=\sqrt{400*29}=\sqrt{400}*\sqrt{29}=20\sqrt{29}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-20\sqrt{29}}{2*200}=\frac{-100-20\sqrt{29}}{400}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+20\sqrt{29}}{2*200}=\frac{-100+20\sqrt{29}}{400}
$