3y-2(5y-4)y=1

Solution for 3y-2(5y-4)y=1 equation:

3y-2(5y-4)y=1

We move all terms to the left:

3y-2(5y-4)y-(1)=0

We multiply parentheses

-10y^2+3y+8y-1=0

We add all the numbers together, and all the variables

-10y^2+11y-1=0

a = -10; b = 11; c = -1;
Δ = b2-4ac
Δ = 112-4·(-10)·(-1)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-9}{2*-10}=\frac{-20}{-20}
=1
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+9}{2*-10}=\frac{-2}{-20}
=1/10
$