-2y(5y-9)-y=-2(y-3)

Solution for -2y(5y-9)-y=-2(y-3) equation:

-2y(5y-9)-y=-2(y-3)

We move all terms to the left:

-2y(5y-9)-y-(-2(y-3))=0

We add all the numbers together, and all the variables

-1y-2y(5y-9)-(-2(y-3))=0

We multiply parentheses

-10y^2-1y+18y-(-2(y-3))=0


We calculate terms in parentheses: -(-2(y-3)), so:

-2(y-3)

We multiply parentheses

-2y+6

Back to the equation:

-(-2y+6)


We add all the numbers together, and all the variables

-10y^2+17y-(-2y+6)=0

We get rid of parentheses

-10y^2+17y+2y-6=0

We add all the numbers together, and all the variables

-10y^2+19y-6=0

a = -10; b = 19; c = -6;
Δ = b2-4ac
Δ = 192-4·(-10)·(-6)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-11}{2*-10}=\frac{-30}{-20}
=1+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+11}{2*-10}=\frac{-8}{-20}
=2/5
$