(7y+2)(7y+2)=9

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

(7y+2)(7y+2)=9

We move all terms to the left:

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

We multiply parentheses ..

(+49y^2+14y+14y+4)-9=0

We get rid of parentheses

49y^2+14y+14y+4-9=0

We add all the numbers together, and all the variables

49y^2+28y-5=0

a = 49; b = 28; c = -5;
Δ = b2-4ac
Δ = 282-4·49·(-5)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-42}{2*49}=\frac{-70}{98}
=-5/7
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+42}{2*49}=\frac{14}{98}
=1/7
$