5(8-1y)2y=-2

Solution for 5(8-1y)2y=-2 equation:

5(8-1y)2y=-2

We move all terms to the left:

5(8-1y)2y-(-2)=0

We add all the numbers together, and all the variables

5(-1y+8)2y-(-2)=0

We add all the numbers together, and all the variables

5(-1y+8)2y+2=0

We multiply parentheses

-10y^2+80y+2=0

a = -10; b = 80; c = +2;
Δ = b2-4ac
Δ = 802-4·(-10)·2
Δ = 6480
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:

$\sqrt{\Delta}=\sqrt{6480}=\sqrt{1296*5}=\sqrt{1296}*\sqrt{5}=36\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-36\sqrt{5}}{2*-10}=\frac{-80-36\sqrt{5}}{-20}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+36\sqrt{5}}{2*-10}=\frac{-80+36\sqrt{5}}{-20}
$