-2500+5000x-750x^2=0

Solution for -2500+5000x-750x^2=0 equation:

-2500+5000x-750x^2=0

a = -750; b = 5000; c = -2500;
Δ = b2-4ac
Δ = 50002-4·(-750)·(-2500)
Δ = 17500000
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:

$\sqrt{\Delta}=\sqrt{17500000}=\sqrt{250000*70}=\sqrt{250000}*\sqrt{70}=500\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5000)-500\sqrt{70}}{2*-750}=\frac{-5000-500\sqrt{70}}{-1500}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5000)+500\sqrt{70}}{2*-750}=\frac{-5000+500\sqrt{70}}{-1500}
$