x+x^2/2=0.05

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

x+x^2/2=0.05

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

x^2+x*2-0.1=0

Wy multiply elements

x^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}
$