1500x^2+3500x-78=0

Solution for 1500x^2+3500x-78=0 equation:

1500x^2+3500x-78=0

a = 1500; b = 3500; c = -78;
Δ = b2-4ac
Δ = 35002-4·1500·(-78)
Δ = 12718000
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:

$\sqrt{\Delta}=\sqrt{12718000}=\sqrt{400*31795}=\sqrt{400}*\sqrt{31795}=20\sqrt{31795}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3500)-20\sqrt{31795}}{2*1500}=\frac{-3500-20\sqrt{31795}}{3000}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3500)+20\sqrt{31795}}{2*1500}=\frac{-3500+20\sqrt{31795}}{3000}
$