X(2x+3)=x^2+1

Solution for X(2x+3)=x^2+1 equation:

X(2X+3)=X^2+1

We move all terms to the left:

X(2X+3)-(X^2+1)=0

We multiply parentheses

2X^2+3X-(X^2+1)=0

We get rid of parentheses

2X^2-X^2+3X-1=0

We add all the numbers together, and all the variables

X^2+3X-1=0

a = 1; b = 3; c = -1;
Δ = b2-4ac
Δ = 32-4·1·(-1)
Δ = 13
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{13}}{2*1}=\frac{-3-\sqrt{13}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{13}}{2*1}=\frac{-3+\sqrt{13}}{2}
$