2x^2-24x=5

Solution for 2x^2-24x=5 equation:

2x^2-24x=5

We move all terms to the left:

2x^2-24x-(5)=0

a = 2; b = -24; c = -5;
Δ = b2-4ac
Δ = -242-4·2·(-5)
Δ = 616
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:

$\sqrt{\Delta}=\sqrt{616}=\sqrt{4*154}=\sqrt{4}*\sqrt{154}=2\sqrt{154}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{154}}{2*2}=\frac{24-2\sqrt{154}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{154}}{2*2}=\frac{24+2\sqrt{154}}{4}
$