5/8x+1/9x=39

Solution for 5/8x+1/9x=39 equation:

5/8x+1/9x=39

We move all terms to the left:

5/8x+1/9x-(39)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We calculate fractions


45x/72x^2+8x/72x^2-39=0

We multiply all the terms by the denominator


45x+8x-39*72x^2=0

We add all the numbers together, and all the variables

53x-39*72x^2=0

Wy multiply elements

-2808x^2+53x=0

a = -2808; b = 53; c = 0;
Δ = b2-4ac
Δ = 532-4·(-2808)·0
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(53)-53}{2*-2808}=\frac{-106}{-5616}
=53/2808
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(53)+53}{2*-2808}=\frac{0}{-5616}
=0
$