2x^2-24x-9=0

Solution for 2x^2-24x-9=0 equation:

2x^2-24x-9=0

a = 2; b = -24; c = -9;
Δ = b2-4ac
Δ = -242-4·2·(-9)
Δ = 648
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:

$\sqrt{\Delta}=\sqrt{648}=\sqrt{324*2}=\sqrt{324}*\sqrt{2}=18\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-18\sqrt{2}}{2*2}=\frac{24-18\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+18\sqrt{2}}{2*2}=\frac{24+18\sqrt{2}}{4}
$