6x^2-4=2x+16

Solution for 6x^2-4=2x+16 equation:

6x^2-4=2x+16

We move all terms to the left:

6x^2-4-(2x+16)=0

We get rid of parentheses

6x^2-2x-16-4=0

We add all the numbers together, and all the variables

6x^2-2x-20=0

a = 6; b = -2; c = -20;
Δ = b2-4ac
Δ = -22-4·6·(-20)
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*6}=\frac{-20}{12}
=-1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+22}{2*6}=\frac{24}{12}
=2
$