(3/2)(y+9)=30

Solution for (3/2)(y+9)=30 equation:

(3/2)(y+9)=30

We move all terms to the left:

(3/2)(y+9)-(30)=0


Domain of the equation: 2)(y+9)!=0

y∈R


We add all the numbers together, and all the variables

(+3/2)(y+9)-30=0

We multiply parentheses ..

(+3y^2+3/2*9)-30=0

We multiply all the terms by the denominator


(+3y^2+3-30*2*9)=0

We get rid of parentheses

3y^2+3-30*2*9=0

We add all the numbers together, and all the variables

3y^2-537=0

a = 3; b = 0; c = -537;
Δ = b2-4ac
Δ = 02-4·3·(-537)
Δ = 6444
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:

$\sqrt{\Delta}=\sqrt{6444}=\sqrt{36*179}=\sqrt{36}*\sqrt{179}=6\sqrt{179}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{179}}{2*3}=\frac{0-6\sqrt{179}}{6}
=-\frac{6\sqrt{179}}{6}
=-\sqrt{179}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{179}}{2*3}=\frac{0+6\sqrt{179}}{6}
=\frac{6\sqrt{179}}{6}
=\sqrt{179}
$