x*x+2=3*x*x-16

Solution for x*x+2=3*x*x-16 equation:

x*x+2=3x*x-16

We move all terms to the left:

x*x+2-(3x*x-16)=0

Wy multiply elements

x^2-(3x*x-16)+2=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2-3x*x+18=0

Wy multiply elements

x^2-3x^2+18=0

We add all the numbers together, and all the variables

-2x^2+18=0

a = -2; b = 0; c = +18;
Δ = b2-4ac
Δ = 02-4·(-2)·18
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12}{2*-2}=\frac{-12}{-4}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12}{2*-2}=\frac{12}{-4}
=-3
$