1/4x+3=3/4x+1x

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

1/4x+3=3/4x+1x

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 4x+1x)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

-4x^2+12x-2=0

a = -4; b = 12; c = -2;
Δ = b2-4ac
Δ = 122-4·(-4)·(-2)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{7}}{2*-4}=\frac{-12-4\sqrt{7}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{7}}{2*-4}=\frac{-12+4\sqrt{7}}{-8}
$