2(w)(w+7)=78

Solution for 2(w)(w+7)=78 equation:

2(w)(w+7)=78

We move all terms to the left:

2(w)(w+7)-(78)=0

We multiply parentheses

2w^2+14w-78=0

a = 2; b = 14; c = -78;
Δ = b2-4ac
Δ = 142-4·2·(-78)
Δ = 820
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:

$\sqrt{\Delta}=\sqrt{820}=\sqrt{4*205}=\sqrt{4}*\sqrt{205}=2\sqrt{205}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{205}}{2*2}=\frac{-14-2\sqrt{205}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{205}}{2*2}=\frac{-14+2\sqrt{205}}{4}
$