3.4-4x=1/4x

Solution for 3.4-4x=1/4x equation:

3.4-4x=1/4x

We move all terms to the left:

3.4-4x-(1/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-4x-(+1/4x)+3.4=0

We get rid of parentheses

-4x-1/4x+3.4=0

We multiply all the terms by the denominator


-4x*4x+(3.4)*4x-1=0

We multiply parentheses

-4x*4x+13.6x-1=0

Wy multiply elements

-16x^2+13.6x-1=0

a = -16; b = 13.6; c = -1;
Δ = b2-4ac
Δ = 13.62-4·(-16)·(-1)
Δ = 120.96
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{-(13.6)-\sqrt{120.96}}{2*-16}=\frac{-13.6-\sqrt{120.96}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13.6)+\sqrt{120.96}}{2*-16}=\frac{-13.6+\sqrt{120.96}}{-32}
$