y(2y+7)/(2y+7)=3

Solution for y(2y+7)/(2y+7)=3 equation:

y(2y+7)/(2y+7)=3

We move all terms to the left:

y(2y+7)/(2y+7)-(3)=0


Domain of the equation: (2y+7)!=0

We move all terms containing y to the left, all other terms to the right

2y!=-7

y!=-7/2

y!=-3+1/2

y∈R


We multiply all the terms by the denominator


y(2y+7)-3*(2y+7)=0

We multiply parentheses

2y^2+7y-6y-21=0

We add all the numbers together, and all the variables

2y^2+y-21=0

a = 2; b = 1; c = -21;
Δ = b2-4ac
Δ = 12-4·2·(-21)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-13}{2*2}=\frac{-14}{4}
=-3+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+13}{2*2}=\frac{12}{4}
=3
$