7/8x-4/9x=1/4

Solution for 7/8x-4/9x=1/4 equation:

7/8x-4/9x=1/4

We move all terms to the left:

7/8x-4/9x-(1/4)=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

7/8x-4/9x-(+1/4)=0

We get rid of parentheses

7/8x-4/9x-1/4=0

We calculate fractions


(-648x^2)/1152x^2+1008x/1152x^2+(-512x)/1152x^2=0

We multiply all the terms by the denominator


(-648x^2)+1008x+(-512x)=0

We get rid of parentheses

-648x^2+1008x-512x=0

We add all the numbers together, and all the variables

-648x^2+496x=0

a = -648; b = 496; c = 0;
Δ = b2-4ac
Δ = 4962-4·(-648)·0
Δ = 246016
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{246016}=496$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(496)-496}{2*-648}=\frac{-992}{-1296}
=62/81
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(496)+496}{2*-648}=\frac{0}{-1296}
=0
$