7y-y^2=12

Solution for 7y-y^2=12 equation:

7y-y^2=12

We move all terms to the left:

7y-y^2-(12)=0

We add all the numbers together, and all the variables

-1y^2+7y-12=0

a = -1; b = 7; c = -12;
Δ = b2-4ac
Δ = 72-4·(-1)·(-12)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-1}{2*-1}=\frac{-8}{-2}
=+4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+1}{2*-1}=\frac{-6}{-2}
=+3
$