7(y-7)+2y(y+5)=16

Solution for 7(y-7)+2y(y+5)=16 equation:

7(y-7)+2y(y+5)=16

We move all terms to the left:

7(y-7)+2y(y+5)-(16)=0

We multiply parentheses

2y^2+7y+10y-49-16=0

We add all the numbers together, and all the variables

2y^2+17y-65=0

a = 2; b = 17; c = -65;
Δ = b2-4ac
Δ = 172-4·2·(-65)
Δ = 809
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{809}}{2*2}=\frac{-17-\sqrt{809}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{809}}{2*2}=\frac{-17+\sqrt{809}}{4}
$