9y^2-16y+3=0

Solution for 9y^2-16y+3=0 equation:

9y^2-16y+3=0

a = 9; b = -16; c = +3;
Δ = b2-4ac
Δ = -162-4·9·3
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{37}}{2*9}=\frac{16-2\sqrt{37}}{18}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{37}}{2*9}=\frac{16+2\sqrt{37}}{18}
$