0=6x^2+31x-30

Solution for 0=6x^2+31x-30 equation:

0=6x^2+31x-30

We move all terms to the left:

0-(6x^2+31x-30)=0

We add all the numbers together, and all the variables

-(6x^2+31x-30)=0

We get rid of parentheses

-6x^2-31x+30=0

a = -6; b = -31; c = +30;
Δ = b2-4ac
Δ = -312-4·(-6)·30
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-41}{2*-6}=\frac{-10}{-12}
=5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+41}{2*-6}=\frac{72}{-12}
=-6
$