0=5x^2+2x-9

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

0=5x^2+2x-9

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

a = -5; b = -2; c = +9;
Δ = b2-4ac
Δ = -22-4·(-5)·9
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{46}}{2*-5}=\frac{2-2\sqrt{46}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{46}}{2*-5}=\frac{2+2\sqrt{46}}{-10}
$