3x2-6=2x+34

Solution for 3x2-6=2x+34 equation:

3x^2-6=2x+34

We move all terms to the left:

3x^2-6-(2x+34)=0

We get rid of parentheses

3x^2-2x-34-6=0

We add all the numbers together, and all the variables

3x^2-2x-40=0

a = 3; b = -2; c = -40;
Δ = b2-4ac
Δ = -22-4·3·(-40)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-22}{2*3}=\frac{-20}{6}
=-3+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+22}{2*3}=\frac{24}{6}
=4
$