8y(6+y)=-38

Solution for 8y(6+y)=-38 equation:

8y(6+y)=-38

We move all terms to the left:

8y(6+y)-(-38)=0

We add all the numbers together, and all the variables

8y(y+6)-(-38)=0

We add all the numbers together, and all the variables

8y(y+6)+38=0

We multiply parentheses

8y^2+48y+38=0

a = 8; b = 48; c = +38;
Δ = b2-4ac
Δ = 482-4·8·38
Δ = 1088
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:

$\sqrt{\Delta}=\sqrt{1088}=\sqrt{64*17}=\sqrt{64}*\sqrt{17}=8\sqrt{17}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-8\sqrt{17}}{2*8}=\frac{-48-8\sqrt{17}}{16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+8\sqrt{17}}{2*8}=\frac{-48+8\sqrt{17}}{16}
$