2(x+3)=3x^2+14x+8

Solution for 2(x+3)=3x^2+14x+8 equation:

2(x+3)=3x^2+14x+8

We move all terms to the left:

2(x+3)-(3x^2+14x+8)=0

We multiply parentheses

2x-(3x^2+14x+8)+6=0

We get rid of parentheses

-3x^2+2x-14x-8+6=0

We add all the numbers together, and all the variables

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

a = -3; b = -12; c = -2;
Δ = b2-4ac
Δ = -122-4·(-3)·(-2)
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{30}}{2*-3}=\frac{12-2\sqrt{30}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{30}}{2*-3}=\frac{12+2\sqrt{30}}{-6}
$