1/6(18y+12)-9=-1/2(2y-18)

Solution for 1/6(18y+12)-9=-1/2(2y-18) equation:

1/6(18y+12)-9=-1/2(2y-18)

We move all terms to the left:

1/6(18y+12)-9-(-1/2(2y-18))=0


Domain of the equation: 6(18y+12)!=0

y∈R



Domain of the equation: 2(2y-18))!=0

y∈R


We calculate fractions


(2y2/(6(18y+12)*2(2y-18)))+(-(-6y1)/(6(18y+12)*2(2y-18)))-9=0


We calculate terms in parentheses: +(2y2/(6(18y+12)*2(2y-18))), so:

2y2/(6(18y+12)*2(2y-18))

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: +(-(-6y1)/(6(18y+12)*2(2y-18))), so:

-(-6y1)/(6(18y+12)*2(2y-18))

We add all the numbers together, and all the variables

-(-6y)/(6(18y+12)*2(2y-18))

We multiply all the terms by the denominator


-(-6y)

We get rid of parentheses

6y

Back to the equation:

+(6y)


a = 2; b = 6; c = -9;
Δ = b2-4ac
Δ = 62-4·2·(-9)
Δ = 108
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{3}}{2*2}=\frac{-6-6\sqrt{3}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{3}}{2*2}=\frac{-6+6\sqrt{3}}{4}
$