5=2x^2+24x+68

Solution for 5=2x^2+24x+68 equation:

5=2x^2+24x+68

We move all terms to the left:

5-(2x^2+24x+68)=0

We get rid of parentheses

-2x^2-24x-68+5=0

We add all the numbers together, and all the variables

-2x^2-24x-63=0

a = -2; b = -24; c = -63;
Δ = b2-4ac
Δ = -242-4·(-2)·(-63)
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-6\sqrt{2}}{2*-2}=\frac{24-6\sqrt{2}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+6\sqrt{2}}{2*-2}=\frac{24+6\sqrt{2}}{-4}
$