x^2-24x-306=0

Solution for x^2-24x-306=0 equation:

x^2-24x-306=0

a = 1; b = -24; c = -306;
Δ = b2-4ac
Δ = -242-4·1·(-306)
Δ = 1800
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:

$\sqrt{\Delta}=\sqrt{1800}=\sqrt{900*2}=\sqrt{900}*\sqrt{2}=30\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-30\sqrt{2}}{2*1}=\frac{24-30\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+30\sqrt{2}}{2*1}=\frac{24+30\sqrt{2}}{2}
$