y*(y+5)+y=40

Solution for y*(y+5)+y=40 equation:

y(y+5)+y=40

We move all terms to the left:

y(y+5)+y-(40)=0

We add all the numbers together, and all the variables

y+y(y+5)-40=0

We multiply parentheses

y^2+y+5y-40=0

We add all the numbers together, and all the variables

y^2+6y-40=0

a = 1; b = 6; c = -40;
Δ = b2-4ac
Δ = 62-4·1·(-40)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-14}{2*1}=\frac{-20}{2}
=-10
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+14}{2*1}=\frac{8}{2}
=4
$