4y^2-9y=-2

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

4y^2-9y=-2

We move all terms to the left:

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

We add all the numbers together, and all the variables

4y^2-9y+2=0

a = 4; b = -9; c = +2;
Δ = b2-4ac
Δ = -92-4·4·2
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*4}=\frac{2}{8}
=1/4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+7}{2*4}=\frac{16}{8}
=2
$