3/8x-x=0.4

Solution for 3/8x-x=0.4 equation:

3/8x-x=0.4

We move all terms to the left:

3/8x-x-(0.4)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+3/8x-0.4=0

We multiply all the terms by the denominator


-1x*8x-(0.4)*8x+3=0

We multiply parentheses

-1x*8x-3.2x+3=0

Wy multiply elements

-8x^2-3.2x+3=0

a = -8; b = -3.2; c = +3;
Δ = b2-4ac
Δ = -3.22-4·(-8)·3
Δ = 106.24
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{-(-3.2)-\sqrt{106.24}}{2*-8}=\frac{3.2-\sqrt{106.24}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3.2)+\sqrt{106.24}}{2*-8}=\frac{3.2+\sqrt{106.24}}{-16}
$