100x^2+300x-200=0

Solution for 100x^2+300x-200=0 equation:

100x^2+300x-200=0

a = 100; b = 300; c = -200;
Δ = b2-4ac
Δ = 3002-4·100·(-200)
Δ = 170000
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:

$\sqrt{\Delta}=\sqrt{170000}=\sqrt{10000*17}=\sqrt{10000}*\sqrt{17}=100\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(300)-100\sqrt{17}}{2*100}=\frac{-300-100\sqrt{17}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(300)+100\sqrt{17}}{2*100}=\frac{-300+100\sqrt{17}}{200}
$