4/6x+8=29+1/5x

Solution for 4/6x+8=29+1/5x equation:

4/6x+8=29+1/5x

We move all terms to the left:

4/6x+8-(29+1/5x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4/6x-(1/5x+29)+8=0

We get rid of parentheses

4/6x-1/5x-29+8=0

We calculate fractions


20x/30x^2+(-6x)/30x^2-29+8=0

We add all the numbers together, and all the variables

20x/30x^2+(-6x)/30x^2-21=0

We multiply all the terms by the denominator


20x+(-6x)-21*30x^2=0

Wy multiply elements

-630x^2+20x+(-6x)=0

We get rid of parentheses

-630x^2+20x-6x=0

We add all the numbers together, and all the variables

-630x^2+14x=0

a = -630; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-630)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-630}=\frac{-28}{-1260}
=1/45
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-630}=\frac{0}{-1260}
=0
$