6=2(y+8)7y

Solution for 6=2(y+8)7y equation:

6=2(y+8)7y

We move all terms to the left:

6-(2(y+8)7y)=0


We calculate terms in parentheses: -(2(y+8)7y), so:

2(y+8)7y

We multiply parentheses

14y^2+112y

Back to the equation:

-(14y^2+112y)


We get rid of parentheses

-14y^2-112y+6=0

a = -14; b = -112; c = +6;
Δ = b2-4ac
Δ = -1122-4·(-14)·6
Δ = 12880
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:

$\sqrt{\Delta}=\sqrt{12880}=\sqrt{16*805}=\sqrt{16}*\sqrt{805}=4\sqrt{805}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-112)-4\sqrt{805}}{2*-14}=\frac{112-4\sqrt{805}}{-28}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+4\sqrt{805}}{2*-14}=\frac{112+4\sqrt{805}}{-28}
$