7y*(2y+6)=(7y+2y)+6

Solution for 7y*(2y+6)=(7y+2y)+6 equation:

7y(2y+6)=(7y+2y)+6

We move all terms to the left:

7y(2y+6)-((7y+2y)+6)=0

We add all the numbers together, and all the variables

7y(2y+6)-((+9y)+6)=0

We multiply parentheses

14y^2+42y-((+9y)+6)=0


We calculate terms in parentheses: -((+9y)+6), so:

(+9y)+6

We get rid of parentheses

9y+6

Back to the equation:

-(9y+6)


We get rid of parentheses

14y^2+42y-9y-6=0

We add all the numbers together, and all the variables

14y^2+33y-6=0

a = 14; b = 33; c = -6;
Δ = b2-4ac
Δ = 332-4·14·(-6)
Δ = 1425
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:

$\sqrt{\Delta}=\sqrt{1425}=\sqrt{25*57}=\sqrt{25}*\sqrt{57}=5\sqrt{57}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-5\sqrt{57}}{2*14}=\frac{-33-5\sqrt{57}}{28}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+5\sqrt{57}}{2*14}=\frac{-33+5\sqrt{57}}{28}
$