6x2-2=34-x

Solution for 6x2-2=34-x equation:

6x^2-2=34-x

We move all terms to the left:

6x^2-2-(34-x)=0

We add all the numbers together, and all the variables

6x^2-(-1x+34)-2=0

We get rid of parentheses

6x^2+1x-34-2=0

We add all the numbers together, and all the variables

6x^2+x-36=0

a = 6; b = 1; c = -36;
Δ = b2-4ac
Δ = 12-4·6·(-36)
Δ = 865
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{865}}{2*6}=\frac{-1-\sqrt{865}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{865}}{2*6}=\frac{-1+\sqrt{865}}{12}
$