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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x+8)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


24x/18x^2+(-3x)/18x^2-8+7=0

We add all the numbers together, and all the variables

24x/18x^2+(-3x)/18x^2-1=0

We multiply all the terms by the denominator


24x+(-3x)-1*18x^2=0

Wy multiply elements

-18x^2+24x+(-3x)=0

We get rid of parentheses

-18x^2+24x-3x=0

We add all the numbers together, and all the variables

-18x^2+21x=0

a = -18; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·(-18)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*-18}=\frac{-42}{-36}
=1+1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*-18}=\frac{0}{-36}
=0
$