X-3x+4=x^2+4

Solution for X-3x+4=x^2+4 equation:

X-3X+4=X^2+4

We move all terms to the left:

X-3X+4-(X^2+4)=0

We add all the numbers together, and all the variables

-2X-(X^2+4)+4=0

We get rid of parentheses

-X^2-2X-4+4=0

We add all the numbers together, and all the variables

-1X^2-2X=0

a = -1; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-1)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-1}=\frac{0}{-2}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-1}=\frac{4}{-2}
=-2
$