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

Solution for 2y(4y+3)-9=0 equation:

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

We multiply parentheses

8y^2+6y-9=0

a = 8; b = 6; c = -9;
Δ = b2-4ac
Δ = 62-4·8·(-9)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-18}{2*8}=\frac{-24}{16}
=-1+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+18}{2*8}=\frac{12}{16}
=3/4
$