5^1.5=x^2+2x

Solution for 5^1.5=x^2+2x equation:

5^1.5=x^2+2x

We move all terms to the left:

5^1.5-(x^2+2x)=0

We add all the numbers together, and all the variables

-(x^2+2x)+11.180339887499=0

We get rid of parentheses

-x^2-2x+11.180339887499=0

We add all the numbers together, and all the variables

-1x^2-2x+11.180339887499=0

a = -1; b = -2; c = +11.180339887499;
Δ = b2-4ac
Δ = -22-4·(-1)·11.180339887499
Δ = 48.721359549996
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{-(-2)-\sqrt{48.721359549996}}{2*-1}=\frac{2-\sqrt{48.721359549996}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+\sqrt{48.721359549996}}{2*-1}=\frac{2+\sqrt{48.721359549996}}{-2}
$