2(3w-7)+2w(w/4)=66

Solution for 2(3w-7)+2w(w/4)=66 equation:

2(3w-7)+2w(w/4)=66

We move all terms to the left:

2(3w-7)+2w(w/4)-(66)=0

We add all the numbers together, and all the variables

2(3w-7)+2w(+w/4)-66=0

We multiply parentheses

2w^2+6w-14-66=0

We add all the numbers together, and all the variables

2w^2+6w-80=0

a = 2; b = 6; c = -80;
Δ = b2-4ac
Δ = 62-4·2·(-80)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-26}{2*2}=\frac{-32}{4}
=-8
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+26}{2*2}=\frac{20}{4}
=5
$