-2y(-3y+8)=8(5y-12)

Solution for -2y(-3y+8)=8(5y-12) equation:

-2y(-3y+8)=8(5y-12)

We move all terms to the left:

-2y(-3y+8)-(8(5y-12))=0

We multiply parentheses

6y^2-16y-(8(5y-12))=0


We calculate terms in parentheses: -(8(5y-12)), so:

8(5y-12)

We multiply parentheses

40y-96

Back to the equation:

-(40y-96)


We get rid of parentheses

6y^2-16y-40y+96=0

We add all the numbers together, and all the variables

6y^2-56y+96=0

a = 6; b = -56; c = +96;
Δ = b2-4ac
Δ = -562-4·6·96
Δ = 832
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:

$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-8\sqrt{13}}{2*6}=\frac{56-8\sqrt{13}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+8\sqrt{13}}{2*6}=\frac{56+8\sqrt{13}}{12}
$