6/9X-4/5x=-18/9

Solution for 6/9X-4/5x=-18/9 equation:

6/9X-4/5X=-18/9

We move all terms to the left:

6/9X-4/5X-(-18/9)=0


Domain of the equation: 9X!=0

X!=0/9

X!=0

X∈R



Domain of the equation: 5X!=0

X!=0/5

X!=0

X∈R


We add all the numbers together, and all the variables

6/9X-4/5X-(-2)=0

We add all the numbers together, and all the variables

6/9X-4/5X+2=0

We calculate fractions


30X/45X^2+(-36X)/45X^2+2=0

We multiply all the terms by the denominator


30X+(-36X)+2*45X^2=0

Wy multiply elements

90X^2+30X+(-36X)=0

We get rid of parentheses

90X^2+30X-36X=0

We add all the numbers together, and all the variables

90X^2-6X=0

a = 90; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·90·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*90}=\frac{0}{180}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*90}=\frac{12}{180}
=1/15
$