2(y-1)-6y=10-2y(y-4)

Solution for 2(y-1)-6y=10-2y(y-4) equation:

2(y-1)-6y=10-2y(y-4)

We move all terms to the left:

2(y-1)-6y-(10-2y(y-4))=0

We add all the numbers together, and all the variables

-6y+2(y-1)-(10-2y(y-4))=0

We multiply parentheses

-6y+2y-(10-2y(y-4))-2=0


We calculate terms in parentheses: -(10-2y(y-4)), so:

10-2y(y-4)

determiningTheFunctionDomain
-2y(y-4)+10

We multiply parentheses

-2y^2+8y+10

Back to the equation:

-(-2y^2+8y+10)


We add all the numbers together, and all the variables

-(-2y^2+8y+10)-4y-2=0

We get rid of parentheses

2y^2-8y-4y-10-2=0

We add all the numbers together, and all the variables

2y^2-12y-12=0

a = 2; b = -12; c = -12;
Δ = b2-4ac
Δ = -122-4·2·(-12)
Δ = 240
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{15}}{2*2}=\frac{12-4\sqrt{15}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{15}}{2*2}=\frac{12+4\sqrt{15}}{4}
$