3x+1/4x=6

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

3x+1/4x=6

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

12x^2-24x+1=0

a = 12; b = -24; c = +1;
Δ = b2-4ac
Δ = -242-4·12·1
Δ = 528
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:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{33}}{2*12}=\frac{24-4\sqrt{33}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{33}}{2*12}=\frac{24+4\sqrt{33}}{24}
$