y=2(8-y)(5y-2)

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

y=2(8-y)(5y-2)

We move all terms to the left:

y-(2(8-y)(5y-2))=0

We add all the numbers together, and all the variables

y-(2(-1y+8)(5y-2))=0

We multiply parentheses ..

-(2(-5y^2+2y+40y-16))+y=0


We calculate terms in parentheses: -(2(-5y^2+2y+40y-16)), so:

2(-5y^2+2y+40y-16)

We multiply parentheses

-10y^2+4y+80y-32

We add all the numbers together, and all the variables

-10y^2+84y-32

Back to the equation:

-(-10y^2+84y-32)


We get rid of parentheses

10y^2-84y+y+32=0

We add all the numbers together, and all the variables

10y^2-83y+32=0

a = 10; b = -83; c = +32;
Δ = b2-4ac
Δ = -832-4·10·32
Δ = 5609
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{-(-83)-\sqrt{5609}}{2*10}=\frac{83-\sqrt{5609}}{20}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-83)+\sqrt{5609}}{2*10}=\frac{83+\sqrt{5609}}{20}
$