0.05=x^2/2-x

Solution for 0.05=x^2/2-x equation:

0.05=x^2/2-x

We move all terms to the left:

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


Domain of the equation: 2-x)!=0

We move all terms containing x to the left, all other terms to the right

-x)!=-2

x!=-2/1

x!=-2

x∈R


We get rid of parentheses

-x^2/2+x+0.05=0

We multiply all the terms by the denominator


-x^2+x*2+(0.05)*2=0

We add all the numbers together, and all the variables

-1x^2+x*2+0.1=0

Wy multiply elements

-1x^2+2x+0.1=0

a = -1; b = 2; c = +0.1;
Δ = b2-4ac
Δ = 22-4·(-1)·0.1
Δ = 4.4
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{4.4}}{2*-1}=\frac{-2-\sqrt{4.4}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+\sqrt{4.4}}{2*-1}=\frac{-2+\sqrt{4.4}}{-2}
$