3/4x+2=4x

Solution for 3/4x+2=4x equation:

3/4x+2=4x

We move all terms to the left:

3/4x+2-(4x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-4x+3/4x+2=0

We multiply all the terms by the denominator


-4x*4x+2*4x+3=0

Wy multiply elements

-16x^2+8x+3=0

a = -16; b = 8; c = +3;
Δ = b2-4ac
Δ = 82-4·(-16)·3
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-16}{2*-16}=\frac{-24}{-32}
=3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+16}{2*-16}=\frac{8}{-32}
=-1/4
$