0=6x^2+17x+5

Solution for 0=6x^2+17x+5 equation:

0=6x^2+17x+5

We move all terms to the left:

0-(6x^2+17x+5)=0

We add all the numbers together, and all the variables

-(6x^2+17x+5)=0

We get rid of parentheses

-6x^2-17x-5=0

a = -6; b = -17; c = -5;
Δ = b2-4ac
Δ = -172-4·(-6)·(-5)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-13}{2*-6}=\frac{4}{-12}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+13}{2*-6}=\frac{30}{-12}
=-2+1/2
$