Y=X(4+x)

Solution for Y=X(4+x) equation:

=Y(4+Y)

We move all terms to the left:

-(Y(4+Y))=0

We add all the numbers together, and all the variables

-(Y(Y+4))=0


We calculate terms in parentheses: -(Y(Y+4)), so:

Y(Y+4)

We multiply parentheses

Y^2+4Y

Back to the equation:

-(Y^2+4Y)


We get rid of parentheses

-Y^2-4Y=0

We add all the numbers together, and all the variables

-1Y^2-4Y=0

a = -1; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-1)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-1}=\frac{0}{-2}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-1}=\frac{8}{-2}
=-4
$