8y(5y+4)=38

Solution for 8y(5y+4)=38 equation:

8y(5y+4)=38

We move all terms to the left:

8y(5y+4)-(38)=0

We multiply parentheses

40y^2+32y-38=0

a = 40; b = 32; c = -38;
Δ = b2-4ac
Δ = 322-4·40·(-38)
Δ = 7104
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:

$\sqrt{\Delta}=\sqrt{7104}=\sqrt{64*111}=\sqrt{64}*\sqrt{111}=8\sqrt{111}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-8\sqrt{111}}{2*40}=\frac{-32-8\sqrt{111}}{80}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+8\sqrt{111}}{2*40}=\frac{-32+8\sqrt{111}}{80}
$