x^2-5x-1500=0

Solution for x^2-5x-1500=0 equation:

x^2-5x-1500=0

a = 1; b = -5; c = -1500;
Δ = b2-4ac
Δ = -52-4·1·(-1500)
Δ = 6025
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:

$\sqrt{\Delta}=\sqrt{6025}=\sqrt{25*241}=\sqrt{25}*\sqrt{241}=5\sqrt{241}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{241}}{2*1}=\frac{5-5\sqrt{241}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{241}}{2*1}=\frac{5+5\sqrt{241}}{2}
$