y=640-y^2/12

Solution for y=640-y^2/12 equation:

y=640-y^2/12

We move all terms to the left:

y-(640-y^2/12)=0

We get rid of parentheses

y^2/12+y-640=0

We multiply all the terms by the denominator


y^2+y*12-640*12=0

We add all the numbers together, and all the variables

y^2+y*12-7680=0

Wy multiply elements

y^2+12y-7680=0

a = 1; b = 12; c = -7680;
Δ = b2-4ac
Δ = 122-4·1·(-7680)
Δ = 30864
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:

$\sqrt{\Delta}=\sqrt{30864}=\sqrt{16*1929}=\sqrt{16}*\sqrt{1929}=4\sqrt{1929}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{1929}}{2*1}=\frac{-12-4\sqrt{1929}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{1929}}{2*1}=\frac{-12+4\sqrt{1929}}{2}
$