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+426y-86=0

a = -5; b = 426; c = -86;
Δ = b2-4ac
Δ = 4262-4·(-5)·(-86)
Δ = 179756
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:

$\sqrt{\Delta}=\sqrt{179756}=\sqrt{4*44939}=\sqrt{4}*\sqrt{44939}=2\sqrt{44939}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(426)-2\sqrt{44939}}{2*-5}=\frac{-426-2\sqrt{44939}}{-10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(426)+2\sqrt{44939}}{2*-5}=\frac{-426+2\sqrt{44939}}{-10}
$