0=5x^2+9x-6

Solution for 0=5x^2+9x-6 equation:

0=5x^2+9x-6

We move all terms to the left:

0-(5x^2+9x-6)=0

We add all the numbers together, and all the variables

-(5x^2+9x-6)=0

We get rid of parentheses

-5x^2-9x+6=0

a = -5; b = -9; c = +6;
Δ = b2-4ac
Δ = -92-4·(-5)·6
Δ = 201
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{-(-9)-\sqrt{201}}{2*-5}=\frac{9-\sqrt{201}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{201}}{2*-5}=\frac{9+\sqrt{201}}{-10}
$