y(30+y)=40

Solution for y(30+y)=40 equation:

y(30+y)=40

We move all terms to the left:

y(30+y)-(40)=0

We add all the numbers together, and all the variables

y(y+30)-40=0

We multiply parentheses

y^2+30y-40=0

a = 1; b = 30; c = -40;
Δ = b2-4ac
Δ = 302-4·1·(-40)
Δ = 1060
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:

$\sqrt{\Delta}=\sqrt{1060}=\sqrt{4*265}=\sqrt{4}*\sqrt{265}=2\sqrt{265}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{265}}{2*1}=\frac{-30-2\sqrt{265}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{265}}{2*1}=\frac{-30+2\sqrt{265}}{2}
$