-(2/3)(9y+18)=30

Solution for -(2/3)(9y+18)=30 equation:

-(2/3)(9y+18)=30

We move all terms to the left:

-(2/3)(9y+18)-(30)=0


Domain of the equation: 3)(9y+18)!=0

y∈R


We add all the numbers together, and all the variables

-(+2/3)(9y+18)-30=0

We multiply parentheses ..

-(+18y^2+2/3*18)-30=0

We multiply all the terms by the denominator


-(+18y^2+2-30*3*18)=0

We get rid of parentheses

-18y^2-2+30*3*18=0

We add all the numbers together, and all the variables

-18y^2+1618=0

a = -18; b = 0; c = +1618;
Δ = b2-4ac
Δ = 02-4·(-18)·1618
Δ = 116496
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:

$\sqrt{\Delta}=\sqrt{116496}=\sqrt{144*809}=\sqrt{144}*\sqrt{809}=12\sqrt{809}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{809}}{2*-18}=\frac{0-12\sqrt{809}}{-36}
=-\frac{12\sqrt{809}}{-36}
=-\frac{\sqrt{809}}{-3}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{809}}{2*-18}=\frac{0+12\sqrt{809}}{-36}
=\frac{12\sqrt{809}}{-36}
=\frac{\sqrt{809}}{-3}
$