8+2x=x+0.2x^2/2

Solution for 8+2x=x+0.2x^2/2 equation:

8+2x=x+0.2x^2/2

We move all terms to the left:

8+2x-(x+0.2x^2/2)=0

We get rid of parentheses

-0.2x^2/2-x+2x+8=0

We multiply all the terms by the denominator


-0.2x^2-x*2+2x*2+8*2=0

We add all the numbers together, and all the variables

-0.2x^2-x*2+2x*2+16=0

Wy multiply elements

-0.2x^2-2x+4x+16=0

We add all the numbers together, and all the variables

-0.2x^2+2x+16=0

a = -0.2; b = 2; c = +16;
Δ = b2-4ac
Δ = 22-4·(-0.2)·16
Δ = 16.8
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{16.8}}{2*-0.2}=\frac{-2-\sqrt{16.8}}{-0.4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+\sqrt{16.8}}{2*-0.2}=\frac{-2+\sqrt{16.8}}{-0.4}
$