1/8x+1/9x+1/8=47/36

Solution for 1/8x+1/9x+1/8=47/36 equation:

1/8x+1/9x+1/8=47/36

We move all terms to the left:

1/8x+1/9x+1/8-(47/36)=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 add all the numbers together, and all the variables

1/8x+1/9x+1/8-(+47/36)=0

We get rid of parentheses

1/8x+1/9x+1/8-47/36=0

We calculate fractions


(-243648x^2)/165888x^2+972x/165888x^2+18432x/165888x^2+972x/165888x^2=0

We multiply all the terms by the denominator


(-243648x^2)+972x+18432x+972x=0

We add all the numbers together, and all the variables

(-243648x^2)+20376x=0

We get rid of parentheses

-243648x^2+20376x=0

a = -243648; b = 20376; c = 0;
Δ = b2-4ac
Δ = 203762-4·(-243648)·0
Δ = 415181376
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{415181376}=20376$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20376)-20376}{2*-243648}=\frac{-40752}{-487296}
=283/3384
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20376)+20376}{2*-243648}=\frac{0}{-487296}
=0
$