3/2y-5=15-y

Solution for 3/2y-5=15-y equation:

3/2y-5=15-y

We move all terms to the left:

3/2y-5-(15-y)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

3/2y-(-1y+15)-5=0

We get rid of parentheses

3/2y+1y-15-5=0

We multiply all the terms by the denominator


1y*2y-15*2y-5*2y+3=0

Wy multiply elements

2y^2-30y-10y+3=0

We add all the numbers together, and all the variables

2y^2-40y+3=0

a = 2; b = -40; c = +3;
Δ = b2-4ac
Δ = -402-4·2·3
Δ = 1576
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:

$\sqrt{\Delta}=\sqrt{1576}=\sqrt{4*394}=\sqrt{4}*\sqrt{394}=2\sqrt{394}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-2\sqrt{394}}{2*2}=\frac{40-2\sqrt{394}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+2\sqrt{394}}{2*2}=\frac{40+2\sqrt{394}}{4}
$