3/4x=4+2x

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

3/4x=4+2x

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

3/4x-2x-4=0

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -8; b = -16; c = +3;
Δ = b2-4ac
Δ = -162-4·(-8)·3
Δ = 352
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{22}}{2*-8}=\frac{16-4\sqrt{22}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{22}}{2*-8}=\frac{16+4\sqrt{22}}{-16}
$