72y-108=6y(12-18y)

Solution for 72y-108=6y(12-18y) equation:

72y-108=6y(12-18y)

We move all terms to the left:

72y-108-(6y(12-18y))=0

We add all the numbers together, and all the variables

72y-(6y(-18y+12))-108=0


We calculate terms in parentheses: -(6y(-18y+12)), so:

6y(-18y+12)

We multiply parentheses

-108y^2+72y

Back to the equation:

-(-108y^2+72y)


We get rid of parentheses

108y^2-72y+72y-108=0

We add all the numbers together, and all the variables

108y^2-108=0

a = 108; b = 0; c = -108;
Δ = b2-4ac
Δ = 02-4·108·(-108)
Δ = 46656
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{46656}=216$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-216}{2*108}=\frac{-216}{216}
=-1
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+216}{2*108}=\frac{216}{216}
=1
$