x^2+52x-7300=0

Solution for x^2+52x-7300=0 equation:

x^2+52x-7300=0

a = 1; b = 52; c = -7300;
Δ = b2-4ac
Δ = 522-4·1·(-7300)
Δ = 31904
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:

$\sqrt{\Delta}=\sqrt{31904}=\sqrt{16*1994}=\sqrt{16}*\sqrt{1994}=4\sqrt{1994}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-4\sqrt{1994}}{2*1}=\frac{-52-4\sqrt{1994}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+4\sqrt{1994}}{2*1}=\frac{-52+4\sqrt{1994}}{2}
$