3y-5y(2y-6)=8y-2(9y-6)

Solution for 3y-5y(2y-6)=8y-2(9y-6) equation:

3y-5y(2y-6)=8y-2(9y-6)

We move all terms to the left:

3y-5y(2y-6)-(8y-2(9y-6))=0

We multiply parentheses

-10y^2+3y+30y-(8y-2(9y-6))=0


We calculate terms in parentheses: -(8y-2(9y-6)), so:

8y-2(9y-6)

We multiply parentheses

8y-18y+12

We add all the numbers together, and all the variables

-10y+12

Back to the equation:

-(-10y+12)


We add all the numbers together, and all the variables

-10y^2+33y-(-10y+12)=0

We get rid of parentheses

-10y^2+33y+10y-12=0

We add all the numbers together, and all the variables

-10y^2+43y-12=0

a = -10; b = 43; c = -12;
Δ = b2-4ac
Δ = 432-4·(-10)·(-12)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(43)-37}{2*-10}=\frac{-80}{-20}
=+4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+37}{2*-10}=\frac{-6}{-20}
=3/10
$