3x^2-4=6x-x^2

Solution for 3x^2-4=6x-x^2 equation:

3x^2-4=6x-x^2

We move all terms to the left:

3x^2-4-(6x-x^2)=0

We get rid of parentheses

3x^2+x^2-6x-4=0

We add all the numbers together, and all the variables

4x^2-6x-4=0

a = 4; b = -6; c = -4;
Δ = b2-4ac
Δ = -62-4·4·(-4)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-10}{2*4}=\frac{-4}{8}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+10}{2*4}=\frac{16}{8}
=2
$