X^2+27x-13500=0

Solution for X^2+27x-13500=0 equation:

X^2+27X-13500=0

a = 1; b = 27; c = -13500;
Δ = b2-4ac
Δ = 272-4·1·(-13500)
Δ = 54729
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:

$\sqrt{\Delta}=\sqrt{54729}=\sqrt{9*6081}=\sqrt{9}*\sqrt{6081}=3\sqrt{6081}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{6081}}{2*1}=\frac{-27-3\sqrt{6081}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{6081}}{2*1}=\frac{-27+3\sqrt{6081}}{2}
$