-4(y-6)2y=2(y+8)

Solution for -4(y-6)2y=2(y+8) equation:

-4(y-6)2y=2(y+8)

We move all terms to the left:

-4(y-6)2y-(2(y+8))=0

We multiply parentheses

-8y^2+48y-(2(y+8))=0


We calculate terms in parentheses: -(2(y+8)), so:

2(y+8)

We multiply parentheses

2y+16

Back to the equation:

-(2y+16)


We get rid of parentheses

-8y^2+48y-2y-16=0

We add all the numbers together, and all the variables

-8y^2+46y-16=0

a = -8; b = 46; c = -16;
Δ = b2-4ac
Δ = 462-4·(-8)·(-16)
Δ = 1604
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:

$\sqrt{\Delta}=\sqrt{1604}=\sqrt{4*401}=\sqrt{4}*\sqrt{401}=2\sqrt{401}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-2\sqrt{401}}{2*-8}=\frac{-46-2\sqrt{401}}{-16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+2\sqrt{401}}{2*-8}=\frac{-46+2\sqrt{401}}{-16}
$