3/4x+1/4x+6/4x+3x=44

Solution for 3/4x+1/4x+6/4x+3x=44 equation:

3/4x+1/4x+6/4x+3x=44

We move all terms to the left:

3/4x+1/4x+6/4x+3x-(44)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

3x+3/4x+1/4x+6/4x-44=0

We multiply all the terms by the denominator


3x*4x-44*4x+3+1+6=0

We add all the numbers together, and all the variables

3x*4x-44*4x+10=0

Wy multiply elements

12x^2-176x+10=0

a = 12; b = -176; c = +10;
Δ = b2-4ac
Δ = -1762-4·12·10
Δ = 30496
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:

$\sqrt{\Delta}=\sqrt{30496}=\sqrt{16*1906}=\sqrt{16}*\sqrt{1906}=4\sqrt{1906}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-176)-4\sqrt{1906}}{2*12}=\frac{176-4\sqrt{1906}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-176)+4\sqrt{1906}}{2*12}=\frac{176+4\sqrt{1906}}{24}
$