3/4x+6=7-1/4x+x

Solution for 3/4x+6=7-1/4x+x equation:

3/4x+6=7-1/4x+x

We move all terms to the left:

3/4x+6-(7-1/4x+x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



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

x∈R


We add all the numbers together, and all the variables

3/4x-(x-1/4x+7)+6=0

We get rid of parentheses

3/4x-x+1/4x-7+6=0

We multiply all the terms by the denominator


-x*4x-7*4x+6*4x+3+1=0

We add all the numbers together, and all the variables

-x*4x-7*4x+6*4x+4=0

Wy multiply elements

-4x^2-28x+24x+4=0

We add all the numbers together, and all the variables

-4x^2-4x+4=0

a = -4; b = -4; c = +4;
Δ = b2-4ac
Δ = -42-4·(-4)·4
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{5}}{2*-4}=\frac{4-4\sqrt{5}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{5}}{2*-4}=\frac{4+4\sqrt{5}}{-8}
$