Y=x(-10+55x)

Solution for Y=x(-10+55x) equation:

=Y(-10+55Y)

We move all terms to the left:

-(Y(-10+55Y))=0

We add all the numbers together, and all the variables

-(Y(55Y-10))=0


We calculate terms in parentheses: -(Y(55Y-10)), so:

Y(55Y-10)

We multiply parentheses

55Y^2-10Y

Back to the equation:

-(55Y^2-10Y)


We get rid of parentheses

-55Y^2+10Y=0

a = -55; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-55)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-55}=\frac{-20}{-110}
=2/11
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-55}=\frac{0}{-110}
=0
$