2.5y+17=-2/3y-21

Solution for 2.5y+17=-2/3y-21 equation:

2.5y+17=-2/3y-21

We move all terms to the left:

2.5y+17-(-2/3y-21)=0


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

y∈R


We get rid of parentheses

2.5y+2/3y+21+17=0

We multiply all the terms by the denominator


(2.5y)*3y+21*3y+17*3y+2=0

We add all the numbers together, and all the variables

(+2.5y)*3y+21*3y+17*3y+2=0

We multiply parentheses

6y^2+21*3y+17*3y+2=0

Wy multiply elements

6y^2+63y+51y+2=0

We add all the numbers together, and all the variables

6y^2+114y+2=0

a = 6; b = 114; c = +2;
Δ = b2-4ac
Δ = 1142-4·6·2
Δ = 12948
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:

$\sqrt{\Delta}=\sqrt{12948}=\sqrt{4*3237}=\sqrt{4}*\sqrt{3237}=2\sqrt{3237}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(114)-2\sqrt{3237}}{2*6}=\frac{-114-2\sqrt{3237}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(114)+2\sqrt{3237}}{2*6}=\frac{-114+2\sqrt{3237}}{12}
$