1/9(18y+27)-5=-1/2(2y-8)

Solution for 1/9(18y+27)-5=-1/2(2y-8) equation:

1/9(18y+27)-5=-1/2(2y-8)

We move all terms to the left:

1/9(18y+27)-5-(-1/2(2y-8))=0


Domain of the equation: 9(18y+27)!=0

y∈R



Domain of the equation: 2(2y-8))!=0

y∈R


We calculate fractions


(2y2/(9(18y+27)*2(2y-8)))+(-(-9y1)/(9(18y+27)*2(2y-8)))-5=0


We calculate terms in parentheses: +(2y2/(9(18y+27)*2(2y-8))), so:

2y2/(9(18y+27)*2(2y-8))

We multiply all the terms by the denominator


2y2

We add all the numbers together, and all the variables

2y^2

Back to the equation:

+(2y^2)



We calculate terms in parentheses: +(-(-9y1)/(9(18y+27)*2(2y-8))), so:

-(-9y1)/(9(18y+27)*2(2y-8))

We add all the numbers together, and all the variables

-(-9y)/(9(18y+27)*2(2y-8))

We multiply all the terms by the denominator


-(-9y)

We get rid of parentheses

9y

Back to the equation:

+(9y)


a = 2; b = 9; c = -5;
Δ = b2-4ac
Δ = 92-4·2·(-5)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-11}{2*2}=\frac{-20}{4}
=-5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+11}{2*2}=\frac{2}{4}
=1/2
$