2/5x-15=5/8x-18

Solution for 2/5x-15=5/8x-18 equation:

2/5x-15=5/8x-18

We move all terms to the left:

2/5x-15-(5/8x-18)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 8x-18)!=0

x∈R


We get rid of parentheses

2/5x-5/8x+18-15=0

We calculate fractions


16x/40x^2+(-25x)/40x^2+18-15=0

We add all the numbers together, and all the variables

16x/40x^2+(-25x)/40x^2+3=0

We multiply all the terms by the denominator


16x+(-25x)+3*40x^2=0

Wy multiply elements

120x^2+16x+(-25x)=0

We get rid of parentheses

120x^2+16x-25x=0

We add all the numbers together, and all the variables

120x^2-9x=0

a = 120; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·120·0
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*120}=\frac{0}{240}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*120}=\frac{18}{240}
=3/40
$