y+6.4y(6.4y)=8+5/9

Solution for y+6.4y(6.4y)=8+5/9 equation:

y+6.4y(6.4y)=8+5/9

We move all terms to the left:

y+6.4y(6.4y)-(8+5/9)=0

We add all the numbers together, and all the variables

y+6.4y(+6.4y)-(5/9+8)=0

We multiply parentheses

36y^2+y-(5/9+8)=0

We get rid of parentheses

36y^2+y-8-5/9=0

We multiply all the terms by the denominator


36y^2*9+y*9-5-8*9=0

We add all the numbers together, and all the variables

36y^2*9+y*9-77=0

Wy multiply elements

324y^2+9y-77=0

a = 324; b = 9; c = -77;
Δ = b2-4ac
Δ = 92-4·324·(-77)
Δ = 99873
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:

$\sqrt{\Delta}=\sqrt{99873}=\sqrt{729*137}=\sqrt{729}*\sqrt{137}=27\sqrt{137}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-27\sqrt{137}}{2*324}=\frac{-9-27\sqrt{137}}{648}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+27\sqrt{137}}{2*324}=\frac{-9+27\sqrt{137}}{648}
$