400=y(y+30)

Solution for 400=y(y+30) equation:

400=y(y+30)

We move all terms to the left:

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


We calculate terms in parentheses: -(y(y+30)), so:

y(y+30)

We multiply parentheses

y^2+30y

Back to the equation:

-(y^2+30y)


We get rid of parentheses

-y^2-30y+400=0

We add all the numbers together, and all the variables

-1y^2-30y+400=0

a = -1; b = -30; c = +400;
Δ = b2-4ac
Δ = -302-4·(-1)·400
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-50}{2*-1}=\frac{-20}{-2}
=+10
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+50}{2*-1}=\frac{80}{-2}
=-40
$