3/8x+8=29+1/5x

Solution for 3/8x+8=29+1/5x equation:

3/8x+8=29+1/5x

We move all terms to the left:

3/8x+8-(29+1/5x)=0


Domain of the equation: 8x!=0

x!=0/8

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

3/8x-(1/5x+29)+8=0

We get rid of parentheses

3/8x-1/5x-29+8=0

We calculate fractions


15x/40x^2+(-8x)/40x^2-29+8=0

We add all the numbers together, and all the variables

15x/40x^2+(-8x)/40x^2-21=0

We multiply all the terms by the denominator


15x+(-8x)-21*40x^2=0

Wy multiply elements

-840x^2+15x+(-8x)=0

We get rid of parentheses

-840x^2+15x-8x=0

We add all the numbers together, and all the variables

-840x^2+7x=0

a = -840; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-840)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-840}=\frac{-14}{-1680}
=1/120
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-840}=\frac{0}{-1680}
=0
$