1/8x+1/9x+1/8=43/72

Solution for 1/8x+1/9x+1/8=43/72 equation:

1/8x+1/9x+1/8=43/72

We move all terms to the left:

1/8x+1/9x+1/8-(43/72)=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-(+43/72)=0

We get rid of parentheses

1/8x+1/9x+1/8-43/72=0

We calculate fractions


(-222912x^2)/331776x^2+4536x/331776x^2+36864x/331776x^2+4536x/331776x^2=0

We multiply all the terms by the denominator


(-222912x^2)+4536x+36864x+4536x=0

We add all the numbers together, and all the variables

(-222912x^2)+45936x=0

We get rid of parentheses

-222912x^2+45936x=0

a = -222912; b = 45936; c = 0;
Δ = b2-4ac
Δ = 459362-4·(-222912)·0
Δ = 2110116096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2110116096}=45936$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45936)-45936}{2*-222912}=\frac{-91872}{-445824}
=319/1548
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45936)+45936}{2*-222912}=\frac{0}{-445824}
=0
$