5-x=x^2/2

Solution for 5-x=x^2/2 equation:

5-x=x^2/2

We move all terms to the left:

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

We add all the numbers together, and all the variables

-1x-(x^2/2)+5=0

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-1x^2-1x*2+10=0

Wy multiply elements

-1x^2-2x+10=0

a = -1; b = -2; c = +10;
Δ = b2-4ac
Δ = -22-4·(-1)·10
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{11}}{2*-1}=\frac{2-2\sqrt{11}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{11}}{2*-1}=\frac{2+2\sqrt{11}}{-2}
$