0=2x^2+24x-74

Solution for 0=2x^2+24x-74 equation:

0=2x^2+24x-74

We move all terms to the left:

0-(2x^2+24x-74)=0

We add all the numbers together, and all the variables

-(2x^2+24x-74)=0

We get rid of parentheses

-2x^2-24x+74=0

a = -2; b = -24; c = +74;
Δ = b2-4ac
Δ = -242-4·(-2)·74
Δ = 1168
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:

$\sqrt{\Delta}=\sqrt{1168}=\sqrt{16*73}=\sqrt{16}*\sqrt{73}=4\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{73}}{2*-2}=\frac{24-4\sqrt{73}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{73}}{2*-2}=\frac{24+4\sqrt{73}}{-4}
$