0=2x^2+18x+11

Solution for 0=2x^2+18x+11 equation:

0=2x^2+18x+11

We move all terms to the left:

0-(2x^2+18x+11)=0

We add all the numbers together, and all the variables

-(2x^2+18x+11)=0

We get rid of parentheses

-2x^2-18x-11=0

a = -2; b = -18; c = -11;
Δ = b2-4ac
Δ = -182-4·(-2)·(-11)
Δ = 236
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:

$\sqrt{\Delta}=\sqrt{236}=\sqrt{4*59}=\sqrt{4}*\sqrt{59}=2\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{59}}{2*-2}=\frac{18-2\sqrt{59}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{59}}{2*-2}=\frac{18+2\sqrt{59}}{-4}
$