3x+1=31/4x

Solution for 3x+1=31/4x equation:

3x+1=31/4x

We move all terms to the left:

3x+1-(31/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x-(+31/4x)+1=0

We get rid of parentheses

3x-31/4x+1=0

We multiply all the terms by the denominator


3x*4x+1*4x-31=0

Wy multiply elements

12x^2+4x-31=0

a = 12; b = 4; c = -31;
Δ = b2-4ac
Δ = 42-4·12·(-31)
Δ = 1504
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:

$\sqrt{\Delta}=\sqrt{1504}=\sqrt{16*94}=\sqrt{16}*\sqrt{94}=4\sqrt{94}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{94}}{2*12}=\frac{-4-4\sqrt{94}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{94}}{2*12}=\frac{-4+4\sqrt{94}}{24}
$