14+2y=16+3/2*y

Solution for 14+2y=16+3/2*y equation:

14+2y=16+3/2y

We move all terms to the left:

14+2y-(16+3/2y)=0


Domain of the equation: 2y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

2y-(3/2y+16)+14=0

We get rid of parentheses

2y-3/2y-16+14=0

We multiply all the terms by the denominator


2y*2y-16*2y+14*2y-3=0

Wy multiply elements

4y^2-32y+28y-3=0

We add all the numbers together, and all the variables

4y^2-4y-3=0

a = 4; b = -4; c = -3;
Δ = b2-4ac
Δ = -42-4·4·(-3)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8}{2*4}=\frac{-4}{8}
=-1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8}{2*4}=\frac{12}{8}
=1+1/2
$