0=6x^2-15x-9

Solution for 0=6x^2-15x-9 equation:

0=6x^2-15x-9

We move all terms to the left:

0-(6x^2-15x-9)=0

We add all the numbers together, and all the variables

-(6x^2-15x-9)=0

We get rid of parentheses

-6x^2+15x+9=0

a = -6; b = 15; c = +9;
Δ = b2-4ac
Δ = 152-4·(-6)·9
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-21}{2*-6}=\frac{-36}{-12}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+21}{2*-6}=\frac{6}{-12}
=-1/2
$