2y2+4=9y

Solution for 2y2+4=9y equation:

2y^2+4=9y

We move all terms to the left:

2y^2+4-(9y)=0

a = 2; b = -9; c = +4;
Δ = b2-4ac
Δ = -92-4·2·4
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-7}{2*2}=\frac{2}{4}
=1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+7}{2*2}=\frac{16}{4}
=4
$