0=6x2-13x-5

Solution for 0=6x2-13x-5 equation:

0=6x^2-13x-5

We move all terms to the left:

0-(6x^2-13x-5)=0

We add all the numbers together, and all the variables

-(6x^2-13x-5)=0

We get rid of parentheses

-6x^2+13x+5=0

a = -6; b = 13; c = +5;
Δ = b2-4ac
Δ = 132-4·(-6)·5
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-17}{2*-6}=\frac{-30}{-12}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+17}{2*-6}=\frac{4}{-12}
=-1/3
$