7y+2y(y-9)=5(y+1)-2

Solution for 7y+2y(y-9)=5(y+1)-2 equation:

7y+2y(y-9)=5(y+1)-2

We move all terms to the left:

7y+2y(y-9)-(5(y+1)-2)=0

We multiply parentheses

2y^2+7y-18y-(5(y+1)-2)=0


We calculate terms in parentheses: -(5(y+1)-2), so:

5(y+1)-2

We multiply parentheses

5y+5-2

We add all the numbers together, and all the variables

5y+3

Back to the equation:

-(5y+3)


We add all the numbers together, and all the variables

2y^2-11y-(5y+3)=0

We get rid of parentheses

2y^2-11y-5y-3=0

We add all the numbers together, and all the variables

2y^2-16y-3=0

a = 2; b = -16; c = -3;
Δ = b2-4ac
Δ = -162-4·2·(-3)
Δ = 280
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{70}}{2*2}=\frac{16-2\sqrt{70}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{70}}{2*2}=\frac{16+2\sqrt{70}}{4}
$