3/8x-6=1/5x+4

Solution for 3/8x-6=1/5x+4 equation:

3/8x-6=1/5x+4

We move all terms to the left:

3/8x-6-(1/5x+4)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 5x+4)!=0

x∈R


We get rid of parentheses

3/8x-1/5x-4-6=0

We calculate fractions


15x/40x^2+(-8x)/40x^2-4-6=0

We add all the numbers together, and all the variables

15x/40x^2+(-8x)/40x^2-10=0

We multiply all the terms by the denominator


15x+(-8x)-10*40x^2=0

Wy multiply elements

-400x^2+15x+(-8x)=0

We get rid of parentheses

-400x^2+15x-8x=0

We add all the numbers together, and all the variables

-400x^2+7x=0

a = -400; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-400)·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*-400}=\frac{-14}{-800}
=7/400
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-400}=\frac{0}{-800}
=0
$