6(x2-3)=x2+46+x2

Solution for 6(x2-3)=x2+46+x2 equation:

6(x2-3)=x2+46+x2

We move all terms to the left:

6(x2-3)-(x2+46+x2)=0

We add all the numbers together, and all the variables

6(+x^2-3)-(+2x^2+46)=0

We multiply parentheses

6x^2-(+2x^2+46)-18=0

We get rid of parentheses

6x^2-2x^2-46-18=0

We add all the numbers together, and all the variables

4x^2-64=0

a = 4; b = 0; c = -64;
Δ = b2-4ac
Δ = 02-4·4·(-64)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32}{2*4}=\frac{-32}{8}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32}{2*4}=\frac{32}{8}
=4
$