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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

3x*4x+7*4x+2=0

Wy multiply elements

12x^2+28x+2=0

a = 12; b = 28; c = +2;
Δ = b2-4ac
Δ = 282-4·12·2
Δ = 688
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:

$\sqrt{\Delta}=\sqrt{688}=\sqrt{16*43}=\sqrt{16}*\sqrt{43}=4\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{43}}{2*12}=\frac{-28-4\sqrt{43}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{43}}{2*12}=\frac{-28+4\sqrt{43}}{24}
$