4/3x-17-5/9x=7

Solution for 4/3x-17-5/9x=7 equation:

4/3x-17-5/9x=7

We move all terms to the left:

4/3x-17-5/9x-(7)=0


Domain of the equation: 3x!=0

x!=0/3

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

4/3x-5/9x-24=0

We calculate fractions


36x/27x^2+(-15x)/27x^2-24=0

We multiply all the terms by the denominator


36x+(-15x)-24*27x^2=0

Wy multiply elements

-648x^2+36x+(-15x)=0

We get rid of parentheses

-648x^2+36x-15x=0

We add all the numbers together, and all the variables

-648x^2+21x=0

a = -648; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·(-648)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*-648}=\frac{-42}{-1296}
=7/216
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*-648}=\frac{0}{-1296}
=0
$