2+2/5x=3/8x-1

Solution for 2+2/5x=3/8x-1 equation:

2+2/5x=3/8x-1

We move all terms to the left:

2+2/5x-(3/8x-1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 8x-1)!=0

x∈R


We get rid of parentheses

2/5x-3/8x+1+2=0

We calculate fractions


16x/40x^2+(-15x)/40x^2+1+2=0

We add all the numbers together, and all the variables

16x/40x^2+(-15x)/40x^2+3=0

We multiply all the terms by the denominator


16x+(-15x)+3*40x^2=0

Wy multiply elements

120x^2+16x+(-15x)=0

We get rid of parentheses

120x^2+16x-15x=0

We add all the numbers together, and all the variables

120x^2+x=0

a = 120; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·120·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*120}=\frac{-2}{240}
=-1/120
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*120}=\frac{0}{240}
=0
$