2(x+8)=3x^2

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

2(x+8)=3x^2

We move all terms to the left:

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

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

We multiply parentheses

-3x^2+2x+16=0

a = -3; b = 2; c = +16;
Δ = b2-4ac
Δ = 22-4·(-3)·16
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-14}{2*-3}=\frac{-16}{-6}
=2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+14}{2*-3}=\frac{12}{-6}
=-2
$