(5y+3)(4y+8)=146

Solution for (5y+3)(4y+8)=146 equation:

(5y+3)(4y+8)=146

We move all terms to the left:

(5y+3)(4y+8)-(146)=0

We multiply parentheses ..

(+20y^2+40y+12y+24)-146=0

We get rid of parentheses

20y^2+40y+12y+24-146=0

We add all the numbers together, and all the variables

20y^2+52y-122=0

a = 20; b = 52; c = -122;
Δ = b2-4ac
Δ = 522-4·20·(-122)
Δ = 12464
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:

$\sqrt{\Delta}=\sqrt{12464}=\sqrt{16*779}=\sqrt{16}*\sqrt{779}=4\sqrt{779}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-4\sqrt{779}}{2*20}=\frac{-52-4\sqrt{779}}{40}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+4\sqrt{779}}{2*20}=\frac{-52+4\sqrt{779}}{40}
$