4y^2-9y=-3

Solution for 4y^2-9y=-3 equation:

4y^2-9y=-3

We move all terms to the left:

4y^2-9y-(-3)=0

We add all the numbers together, and all the variables

4y^2-9y+3=0

a = 4; b = -9; c = +3;
Δ = b2-4ac
Δ = -92-4·4·3
Δ = 33
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{-(-9)-\sqrt{33}}{2*4}=\frac{9-\sqrt{33}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{33}}{2*4}=\frac{9+\sqrt{33}}{8}
$