2x+3(x^2-4)=22

Solution for 2x+3(x^2-4)=22 equation:

2x+3(x^2-4)=22

We move all terms to the left:

2x+3(x^2-4)-(22)=0

We multiply parentheses

3x^2+2x-12-22=0

We add all the numbers together, and all the variables

3x^2+2x-34=0

a = 3; b = 2; c = -34;
Δ = b2-4ac
Δ = 22-4·3·(-34)
Δ = 412
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:

$\sqrt{\Delta}=\sqrt{412}=\sqrt{4*103}=\sqrt{4}*\sqrt{103}=2\sqrt{103}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{103}}{2*3}=\frac{-2-2\sqrt{103}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{103}}{2*3}=\frac{-2+2\sqrt{103}}{6}
$