9/2y+3=3y+13.5

Solution for 9/2y+3=3y+13.5 equation:

9/2y+3=3y+13.5

We move all terms to the left:

9/2y+3-(3y+13.5)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We get rid of parentheses

9/2y-3y-13.5+3=0

We multiply all the terms by the denominator


-3y*2y-(13.5)*2y+3*2y+9=0

We multiply parentheses

-3y*2y-27y+3*2y+9=0

Wy multiply elements

-6y^2-27y+6y+9=0

We add all the numbers together, and all the variables

-6y^2-21y+9=0

a = -6; b = -21; c = +9;
Δ = b2-4ac
Δ = -212-4·(-6)·9
Δ = 657
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:

$\sqrt{\Delta}=\sqrt{657}=\sqrt{9*73}=\sqrt{9}*\sqrt{73}=3\sqrt{73}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{73}}{2*-6}=\frac{21-3\sqrt{73}}{-12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{73}}{2*-6}=\frac{21+3\sqrt{73}}{-12}
$