5x=x2+2

Solution for 5x=x2+2 equation:

5x=x2+2

We move all terms to the left:

5x-(x2+2)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

-x^2+5x-2=0

We add all the numbers together, and all the variables

-1x^2+5x-2=0

a = -1; b = 5; c = -2;
Δ = b2-4ac
Δ = 52-4·(-1)·(-2)
Δ = 17
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{-(5)-\sqrt{17}}{2*-1}=\frac{-5-\sqrt{17}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{17}}{2*-1}=\frac{-5+\sqrt{17}}{-2}
$