Y=3(0.5x-6)(6-30x)

Solution for Y=3(0.5x-6)(6-30x) equation:

=3(0.5Y-6)(6-30Y)

We move all terms to the left:

-(3(0.5Y-6)(6-30Y))=0

We add all the numbers together, and all the variables

-(3(0.5Y-6)(-30Y+6))=0

We multiply parentheses ..

-(3(+0Y^2+0Y+180Y-36))=0


We calculate terms in parentheses: -(3(+0Y^2+0Y+180Y-36)), so:

3(+0Y^2+0Y+180Y-36)

We multiply parentheses

0Y^2+0Y+540Y-108

We add all the numbers together, and all the variables

Y^2+541Y-108

Back to the equation:

-(Y^2+541Y-108)


We get rid of parentheses

-Y^2-541Y+108=0

We add all the numbers together, and all the variables

-1Y^2-541Y+108=0

a = -1; b = -541; c = +108;
Δ = b2-4ac
Δ = -5412-4·(-1)·108
Δ = 293113
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-541)-\sqrt{293113}}{2*-1}=\frac{541-\sqrt{293113}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-541)+\sqrt{293113}}{2*-1}=\frac{541+\sqrt{293113}}{-2}
$