x^2+102x-4000=0

Solution for x^2+102x-4000=0 equation:

x^2+102x-4000=0

a = 1; b = 102; c = -4000;
Δ = b2-4ac
Δ = 1022-4·1·(-4000)
Δ = 26404
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:

$\sqrt{\Delta}=\sqrt{26404}=\sqrt{4*6601}=\sqrt{4}*\sqrt{6601}=2\sqrt{6601}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(102)-2\sqrt{6601}}{2*1}=\frac{-102-2\sqrt{6601}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(102)+2\sqrt{6601}}{2*1}=\frac{-102+2\sqrt{6601}}{2}
$