y^2+9/4=4y

Solution for y^2+9/4=4y equation:

y^2+9/4=4y

We move all terms to the left:

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

We multiply all the terms by the denominator


y^2*4-4y*4+9=0

Wy multiply elements

4y^2-16y+9=0

a = 4; b = -16; c = +9;
Δ = b2-4ac
Δ = -162-4·4·9
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{7}}{2*4}=\frac{16-4\sqrt{7}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{7}}{2*4}=\frac{16+4\sqrt{7}}{8}
$