1.5y+17=-2/3y-21

Solution for 1.5y+17=-2/3y-21 equation:

1.5y+17=-2/3y-21

We move all terms to the left:

1.5y+17-(-2/3y-21)=0


Domain of the equation: 3y-21)!=0

y∈R


We get rid of parentheses

1.5y+2/3y+21+17=0

We multiply all the terms by the denominator


(1.5y)*3y+21*3y+17*3y+2=0

We add all the numbers together, and all the variables

(+1.5y)*3y+21*3y+17*3y+2=0

We multiply parentheses

3y^2+21*3y+17*3y+2=0

Wy multiply elements

3y^2+63y+51y+2=0

We add all the numbers together, and all the variables

3y^2+114y+2=0

a = 3; b = 114; c = +2;
Δ = b2-4ac
Δ = 1142-4·3·2
Δ = 12972
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:

$\sqrt{\Delta}=\sqrt{12972}=\sqrt{4*3243}=\sqrt{4}*\sqrt{3243}=2\sqrt{3243}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(114)-2\sqrt{3243}}{2*3}=\frac{-114-2\sqrt{3243}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(114)+2\sqrt{3243}}{2*3}=\frac{-114+2\sqrt{3243}}{6}
$