28=x-0.2/x-0.4

Solution for 28=x-0.2/x-0.4 equation:

28=x-0.2/x-0.4

We move all terms to the left:

28-(x-0.2/x-0.4)=0


Domain of the equation: x-0.4)!=0

x∈R


We get rid of parentheses

-x+0.2/x+0.4+28=0

We multiply all the terms by the denominator


-x*x+(0.4)*x+28*x+0.2=0

We add all the numbers together, and all the variables

28x-x*x+(0.4)*x+0.2=0

We multiply parentheses

28x-x*x+0.4x+0.2=0

Wy multiply elements

-1x^2+28x+0.4x+0.2=0

We add all the numbers together, and all the variables

-1x^2+28.4x+0.2=0

a = -1; b = 28.4; c = +0.2;
Δ = b2-4ac
Δ = 28.42-4·(-1)·0.2
Δ = 807.36
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{-(28.4)-\sqrt{807.36}}{2*-1}=\frac{-28.4-\sqrt{807.36}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28.4)+\sqrt{807.36}}{2*-1}=\frac{-28.4+\sqrt{807.36}}{-2}
$