2/5x-5/8x=26

Solution for 2/5x-5/8x=26 equation:

2/5x-5/8x=26

We move all terms to the left:

2/5x-5/8x-(26)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We calculate fractions


16x/40x^2+(-25x)/40x^2-26=0

We multiply all the terms by the denominator


16x+(-25x)-26*40x^2=0

Wy multiply elements

-1040x^2+16x+(-25x)=0

We get rid of parentheses

-1040x^2+16x-25x=0

We add all the numbers together, and all the variables

-1040x^2-9x=0

a = -1040; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·(-1040)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*-1040}=\frac{0}{-2080}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*-1040}=\frac{18}{-2080}
=-9/1040
$