-2(w-7)7w=44

Solution for -2(w-7)7w=44 equation:

-2(w-7)7w=44

We move all terms to the left:

-2(w-7)7w-(44)=0

We multiply parentheses

-14w^2+98w-44=0

a = -14; b = 98; c = -44;
Δ = b2-4ac
Δ = 982-4·(-14)·(-44)
Δ = 7140
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{7140}=\sqrt{4*1785}=\sqrt{4}*\sqrt{1785}=2\sqrt{1785}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(98)-2\sqrt{1785}}{2*-14}=\frac{-98-2\sqrt{1785}}{-28}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(98)+2\sqrt{1785}}{2*-14}=\frac{-98+2\sqrt{1785}}{-28}
$