0=5x^2-11x-9

Solution for 0=5x^2-11x-9 equation:

0=5x^2-11x-9

We move all terms to the left:

0-(5x^2-11x-9)=0

We add all the numbers together, and all the variables

-(5x^2-11x-9)=0

We get rid of parentheses

-5x^2+11x+9=0

a = -5; b = 11; c = +9;
Δ = b2-4ac
Δ = 112-4·(-5)·9
Δ = 301
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{-(11)-\sqrt{301}}{2*-5}=\frac{-11-\sqrt{301}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{301}}{2*-5}=\frac{-11+\sqrt{301}}{-10}
$