Y=-5x(x-2)-x

Solution for Y=-5x(x-2)-x equation:

=-5Y(Y-2)-Y

We move all terms to the left:

-(-5Y(Y-2)-Y)=0


We calculate terms in parentheses: -(-5Y(Y-2)-Y), so:

-5Y(Y-2)-Y

We add all the numbers together, and all the variables

-1Y-5Y(Y-2)

We multiply parentheses

-5Y^2-1Y+10Y

We add all the numbers together, and all the variables

-5Y^2+9Y

Back to the equation:

-(-5Y^2+9Y)


We get rid of parentheses

5Y^2-9Y=0

a = 5; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·5·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*5}=\frac{0}{10}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*5}=\frac{18}{10}
=1+4/5
$