5y*(86-y)=86-4y

Solution for 5y*(86-y)=86-4y equation:

5y(86-y)=86-4y

We move all terms to the left:

5y(86-y)-(86-4y)=0

We add all the numbers together, and all the variables

5y(-1y+86)-(-4y+86)=0

We multiply parentheses

-5y^2+430y-(-4y+86)=0

We get rid of parentheses

-5y^2+430y+4y-86=0

We add all the numbers together, and all the variables

-5y^2+434y-86=0

a = -5; b = 434; c = -86;
Δ = b2-4ac
Δ = 4342-4·(-5)·(-86)
Δ = 186636
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:

$\sqrt{\Delta}=\sqrt{186636}=\sqrt{4*46659}=\sqrt{4}*\sqrt{46659}=2\sqrt{46659}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(434)-2\sqrt{46659}}{2*-5}=\frac{-434-2\sqrt{46659}}{-10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(434)+2\sqrt{46659}}{2*-5}=\frac{-434+2\sqrt{46659}}{-10}
$