X^2-20x-2300=0

Solution for X^2-20x-2300=0 equation:

X^2-20X-2300=0

a = 1; b = -20; c = -2300;
Δ = b2-4ac
Δ = -202-4·1·(-2300)
Δ = 9600
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:

$\sqrt{\Delta}=\sqrt{9600}=\sqrt{1600*6}=\sqrt{1600}*\sqrt{6}=40\sqrt{6}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-40\sqrt{6}}{2*1}=\frac{20-40\sqrt{6}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+40\sqrt{6}}{2*1}=\frac{20+40\sqrt{6}}{2}
$