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

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

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

We move all terms to the left:

3x+1/4x+6-(-7)=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+1/4x+13=0

We multiply all the terms by the denominator


3x*4x+13*4x+1=0

Wy multiply elements

12x^2+52x+1=0

a = 12; b = 52; c = +1;
Δ = b2-4ac
Δ = 522-4·12·1
Δ = 2656
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:

$\sqrt{\Delta}=\sqrt{2656}=\sqrt{16*166}=\sqrt{16}*\sqrt{166}=4\sqrt{166}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-4\sqrt{166}}{2*12}=\frac{-52-4\sqrt{166}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+4\sqrt{166}}{2*12}=\frac{-52+4\sqrt{166}}{24}
$