0.1+2x=1/4x+0.5

Solution for 0.1+2x=1/4x+0.5 equation:

0.1+2x=1/4x+0.5

We move all terms to the left:

0.1+2x-(1/4x+0.5)=0


Domain of the equation: 4x+0.5)!=0

x∈R


We get rid of parentheses

2x-1/4x-0.5+0.1=0

We multiply all the terms by the denominator


2x*4x-(0.5)*4x+(0.1)*4x-1=0

We multiply parentheses

2x*4x-2x+0.4x-1=0

Wy multiply elements

8x^2-2x+0.4x-1=0

We add all the numbers together, and all the variables

8x^2-1.6x-1=0

a = 8; b = -1.6; c = -1;
Δ = b2-4ac
Δ = -1.62-4·8·(-1)
Δ = 34.56
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{-(-1.6)-\sqrt{34.56}}{2*8}=\frac{1.6-\sqrt{34.56}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.6)+\sqrt{34.56}}{2*8}=\frac{1.6+\sqrt{34.56}}{16}
$