2x^2+100x-75=0

Solution for 2x^2+100x-75=0 equation:

2x^2+100x-75=0

a = 2; b = 100; c = -75;
Δ = b2-4ac
Δ = 1002-4·2·(-75)
Δ = 10600
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:

$\sqrt{\Delta}=\sqrt{10600}=\sqrt{100*106}=\sqrt{100}*\sqrt{106}=10\sqrt{106}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-10\sqrt{106}}{2*2}=\frac{-100-10\sqrt{106}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+10\sqrt{106}}{2*2}=\frac{-100+10\sqrt{106}}{4}
$