Y=(1-10x)(6x+1)

Solution for Y=(1-10x)(6x+1) equation:

=(1-10Y)(6Y+1)

We move all terms to the left:

-((1-10Y)(6Y+1))=0

We add all the numbers together, and all the variables

-((-10Y+1)(6Y+1))=0

We multiply parentheses ..

-((-60Y^2-10Y+6Y+1))=0


We calculate terms in parentheses: -((-60Y^2-10Y+6Y+1)), so:

(-60Y^2-10Y+6Y+1)

We get rid of parentheses

-60Y^2-10Y+6Y+1

We add all the numbers together, and all the variables

-60Y^2-4Y+1

Back to the equation:

-(-60Y^2-4Y+1)


We get rid of parentheses

60Y^2+4Y-1=0

a = 60; b = 4; c = -1;
Δ = b2-4ac
Δ = 42-4·60·(-1)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-16}{2*60}=\frac{-20}{120}
=-1/6
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+16}{2*60}=\frac{12}{120}
=1/10
$