-10y(4y-8)-3y=-9

Solution for -10y(4y-8)-3y=-9 equation:

-10y(4y-8)-3y=-9

We move all terms to the left:

-10y(4y-8)-3y-(-9)=0

We add all the numbers together, and all the variables

-3y-10y(4y-8)+9=0

We multiply parentheses

-40y^2-3y+80y+9=0

We add all the numbers together, and all the variables

-40y^2+77y+9=0

a = -40; b = 77; c = +9;
Δ = b2-4ac
Δ = 772-4·(-40)·9
Δ = 7369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(77)-\sqrt{7369}}{2*-40}=\frac{-77-\sqrt{7369}}{-80}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(77)+\sqrt{7369}}{2*-40}=\frac{-77+\sqrt{7369}}{-80}
$