4y^2-3y=9

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

4y^2-3y=9

We move all terms to the left:

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

a = 4; b = -3; c = -9;
Δ = b2-4ac
Δ = -32-4·4·(-9)
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{17}}{2*4}=\frac{3-3\sqrt{17}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{17}}{2*4}=\frac{3+3\sqrt{17}}{8}
$