8y+2y(y-7)=3(y+1)-2

Solution for 8y+2y(y-7)=3(y+1)-2 equation:

8y+2y(y-7)=3(y+1)-2

We move all terms to the left:

8y+2y(y-7)-(3(y+1)-2)=0

We multiply parentheses

2y^2+8y-14y-(3(y+1)-2)=0


We calculate terms in parentheses: -(3(y+1)-2), so:

3(y+1)-2

We multiply parentheses

3y+3-2

We add all the numbers together, and all the variables

3y+1

Back to the equation:

-(3y+1)


We add all the numbers together, and all the variables

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

We get rid of parentheses

2y^2-6y-3y-1=0

We add all the numbers together, and all the variables

2y^2-9y-1=0

a = 2; b = -9; c = -1;
Δ = b2-4ac
Δ = -92-4·2·(-1)
Δ = 89
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{-(-9)-\sqrt{89}}{2*2}=\frac{9-\sqrt{89}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{89}}{2*2}=\frac{9+\sqrt{89}}{4}
$