(4y+8)(5y+)=146

Solution for (4y+8)(5y+)=146 equation:

(4y+8)(5y+)=146

We move all terms to the left:

(4y+8)(5y+)-(146)=0

We add all the numbers together, and all the variables

(4y+8)(+5y)-146=0

We multiply parentheses ..

(+20y^2+40y)-146=0

We get rid of parentheses

20y^2+40y-146=0

a = 20; b = 40; c = -146;
Δ = b2-4ac
Δ = 402-4·20·(-146)
Δ = 13280
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:

$\sqrt{\Delta}=\sqrt{13280}=\sqrt{16*830}=\sqrt{16}*\sqrt{830}=4\sqrt{830}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{830}}{2*20}=\frac{-40-4\sqrt{830}}{40}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{830}}{2*20}=\frac{-40+4\sqrt{830}}{40}
$