0=6x^2+17-39

Solution for 0=6x^2+17-39 equation:

0=6x^2+17-39

We move all terms to the left:

0-(6x^2+17-39)=0

We add all the numbers together, and all the variables

-(6x^2+17-39)=0

We get rid of parentheses

-6x^2-17+39=0

We add all the numbers together, and all the variables

-6x^2+22=0

a = -6; b = 0; c = +22;
Δ = b2-4ac
Δ = 02-4·(-6)·22
Δ = 528
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{33}}{2*-6}=\frac{0-4\sqrt{33}}{-12}
=-\frac{4\sqrt{33}}{-12}
=-\frac{\sqrt{33}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{33}}{2*-6}=\frac{0+4\sqrt{33}}{-12}
=\frac{4\sqrt{33}}{-12}
=\frac{\sqrt{33}}{-3}
$