3(8-4y^2)-y^2=11

Solution for 3(8-4y^2)-y^2=11 equation:

3(8-4y^2)-y^2=11

We move all terms to the left:

3(8-4y^2)-y^2-(11)=0

We add all the numbers together, and all the variables

-1y^2+3(8-4y^2)-11=0

We multiply parentheses

-1y^2-12y^2+24-11=0

We add all the numbers together, and all the variables

-13y^2+13=0

a = -13; b = 0; c = +13;
Δ = b2-4ac
Δ = 02-4·(-13)·13
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-26}{2*-13}=\frac{-26}{-26}
=1
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+26}{2*-13}=\frac{26}{-26}
=-1
$