0=2x^2-5x-11

Solution for 0=2x^2-5x-11 equation:

0=2x^2-5x-11

We move all terms to the left:

0-(2x^2-5x-11)=0

We add all the numbers together, and all the variables

-(2x^2-5x-11)=0

We get rid of parentheses

-2x^2+5x+11=0

a = -2; b = 5; c = +11;
Δ = b2-4ac
Δ = 52-4·(-2)·11
Δ = 113
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{113}}{2*-2}=\frac{-5-\sqrt{113}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{113}}{2*-2}=\frac{-5+\sqrt{113}}{-4}
$