2y(9y+1)=4y+8

Solution for 2y(9y+1)=4y+8 equation:

2y(9y+1)=4y+8

We move all terms to the left:

2y(9y+1)-(4y+8)=0

We multiply parentheses

18y^2+2y-(4y+8)=0

We get rid of parentheses

18y^2+2y-4y-8=0

We add all the numbers together, and all the variables

18y^2-2y-8=0

a = 18; b = -2; c = -8;
Δ = b2-4ac
Δ = -22-4·18·(-8)
Δ = 580
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:

$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{145}}{2*18}=\frac{2-2\sqrt{145}}{36}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{145}}{2*18}=\frac{2+2\sqrt{145}}{36}
$