8/9x-5/3x=5

Solution for 8/9x-5/3x=5 equation:

8/9x-5/3x=5

We move all terms to the left:

8/9x-5/3x-(5)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


24x/27x^2+(-45x)/27x^2-5=0

We multiply all the terms by the denominator


24x+(-45x)-5*27x^2=0

Wy multiply elements

-135x^2+24x+(-45x)=0

We get rid of parentheses

-135x^2+24x-45x=0

We add all the numbers together, and all the variables

-135x^2-21x=0

a = -135; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·(-135)·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*-135}=\frac{0}{-270}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*-135}=\frac{42}{-270}
=-7/45
$