5(8-5y)4y=23

Solution for 5(8-5y)4y=23 equation:

5(8-5y)4y=23

We move all terms to the left:

5(8-5y)4y-(23)=0

We add all the numbers together, and all the variables

5(-5y+8)4y-23=0

We multiply parentheses

-100y^2+160y-23=0

a = -100; b = 160; c = -23;
Δ = b2-4ac
Δ = 1602-4·(-100)·(-23)
Δ = 16400
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:

$\sqrt{\Delta}=\sqrt{16400}=\sqrt{400*41}=\sqrt{400}*\sqrt{41}=20\sqrt{41}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-20\sqrt{41}}{2*-100}=\frac{-160-20\sqrt{41}}{-200}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+20\sqrt{41}}{2*-100}=\frac{-160+20\sqrt{41}}{-200}
$