X^2+15x-6500=0

Solution for X^2+15x-6500=0 equation:

X^2+15X-6500=0

a = 1; b = 15; c = -6500;
Δ = b2-4ac
Δ = 152-4·1·(-6500)
Δ = 26225
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:

$\sqrt{\Delta}=\sqrt{26225}=\sqrt{25*1049}=\sqrt{25}*\sqrt{1049}=5\sqrt{1049}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-5\sqrt{1049}}{2*1}=\frac{-15-5\sqrt{1049}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+5\sqrt{1049}}{2*1}=\frac{-15+5\sqrt{1049}}{2}
$