4x+5=x^2-2+3+x^2

Solution for 4x+5=x^2-2+3+x^2 equation:

4x+5=x^2-2+3+x^2

We move all terms to the left:

4x+5-(x^2-2+3+x^2)=0

We get rid of parentheses

-x^2-x^2+4x+2-3+5=0

We add all the numbers together, and all the variables

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

a = -2; b = 4; c = +4;
Δ = b2-4ac
Δ = 42-4·(-2)·4
Δ = 48
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{3}}{2*-2}=\frac{-4-4\sqrt{3}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{3}}{2*-2}=\frac{-4+4\sqrt{3}}{-4}
$