0=2x^2+12x+5

Solution for 0=2x^2+12x+5 equation:

0=2x^2+12x+5

We move all terms to the left:

0-(2x^2+12x+5)=0

We add all the numbers together, and all the variables

-(2x^2+12x+5)=0

We get rid of parentheses

-2x^2-12x-5=0

a = -2; b = -12; c = -5;
Δ = b2-4ac
Δ = -122-4·(-2)·(-5)
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{26}}{2*-2}=\frac{12-2\sqrt{26}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{26}}{2*-2}=\frac{12+2\sqrt{26}}{-4}
$