6y+2y(y-9)=5(y+1)-3

Solution for 6y+2y(y-9)=5(y+1)-3 equation:

6y+2y(y-9)=5(y+1)-3

We move all terms to the left:

6y+2y(y-9)-(5(y+1)-3)=0

We multiply parentheses

2y^2+6y-18y-(5(y+1)-3)=0


We calculate terms in parentheses: -(5(y+1)-3), so:

5(y+1)-3

We multiply parentheses

5y+5-3

We add all the numbers together, and all the variables

5y+2

Back to the equation:

-(5y+2)


We add all the numbers together, and all the variables

2y^2-12y-(5y+2)=0

We get rid of parentheses

2y^2-12y-5y-2=0

We add all the numbers together, and all the variables

2y^2-17y-2=0

a = 2; b = -17; c = -2;
Δ = b2-4ac
Δ = -172-4·2·(-2)
Δ = 305
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{-(-17)-\sqrt{305}}{2*2}=\frac{17-\sqrt{305}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{305}}{2*2}=\frac{17+\sqrt{305}}{4}
$