3/6x-7=1/4x+8

Solution for 3/6x-7=1/4x+8 equation:

3/6x-7=1/4x+8

We move all terms to the left:

3/6x-7-(1/4x+8)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 4x+8)!=0

x∈R


We get rid of parentheses

3/6x-1/4x-8-7=0

We calculate fractions


12x/24x^2+(-6x)/24x^2-8-7=0

We add all the numbers together, and all the variables

12x/24x^2+(-6x)/24x^2-15=0

We multiply all the terms by the denominator


12x+(-6x)-15*24x^2=0

Wy multiply elements

-360x^2+12x+(-6x)=0

We get rid of parentheses

-360x^2+12x-6x=0

We add all the numbers together, and all the variables

-360x^2+6x=0

a = -360; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-360)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-360}=\frac{-12}{-720}
=1/60
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-360}=\frac{0}{-720}
=0
$