0=6x^2+31x+35

Solution for 0=6x^2+31x+35 equation:

0=6x^2+31x+35

We move all terms to the left:

0-(6x^2+31x+35)=0

We add all the numbers together, and all the variables

-(6x^2+31x+35)=0

We get rid of parentheses

-6x^2-31x-35=0

a = -6; b = -31; c = -35;
Δ = b2-4ac
Δ = -312-4·(-6)·(-35)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-11}{2*-6}=\frac{20}{-12}
=-1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+11}{2*-6}=\frac{42}{-12}
=-3+1/2
$