(x-2)23-x(x+1)3=(x-3)(x+3)2-x22

Solution for (x-2)23-x(x+1)3=(x-3)(x+3)2-x22 equation:

(x-2)23-x(x+1)3=(x-3)(x+3)2-x22

We move all terms to the left:

(x-2)23-x(x+1)3-((x-3)(x+3)2-x22)=0

We use the square of the difference formula

x^2+(x-2)23-x(x+1)3+9=0

We multiply parentheses

x^2-3x^2+23x-3x-46+9=0

We add all the numbers together, and all the variables

-2x^2+20x-37=0

a = -2; b = 20; c = -37;
Δ = b2-4ac
Δ = 202-4·(-2)·(-37)
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{26}}{2*-2}=\frac{-20-2\sqrt{26}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{26}}{2*-2}=\frac{-20+2\sqrt{26}}{-4}
$