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

Solution for y(2y+7)/(2y+7)=0 equation:

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

We multiply parentheses

2y^2+7y=0

a = 2; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·2·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*2}=\frac{-14}{4}
=-3+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*2}=\frac{0}{4}
=0
$