3/5X-15=5/8x-16

Solution for 3/5X-15=5/8x-16 equation:

3/5X-15=5/8X-16

We move all terms to the left:

3/5X-15-(5/8X-16)=0


Domain of the equation: 5X!=0

X!=0/5

X!=0

X∈R



Domain of the equation: 8X-16)!=0

X∈R


We get rid of parentheses

3/5X-5/8X+16-15=0

We calculate fractions


24X/40X^2+(-25X)/40X^2+16-15=0

We add all the numbers together, and all the variables

24X/40X^2+(-25X)/40X^2+1=0

We multiply all the terms by the denominator


24X+(-25X)+1*40X^2=0

Wy multiply elements

40X^2+24X+(-25X)=0

We get rid of parentheses

40X^2+24X-25X=0

We add all the numbers together, and all the variables

40X^2-1X=0

a = 40; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·40·0
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*40}=\frac{0}{80}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*40}=\frac{2}{80}
=1/40
$