y=9y^2-16

Solution for y=9y^2-16 equation:

y=9y^2-16

We move all terms to the left:

y-(9y^2-16)=0

We get rid of parentheses

-9y^2+y+16=0

a = -9; b = 1; c = +16;
Δ = b2-4ac
Δ = 12-4·(-9)·16
Δ = 577
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{577}}{2*-9}=\frac{-1-\sqrt{577}}{-18}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{577}}{2*-9}=\frac{-1+\sqrt{577}}{-18}
$