(w-7)(2w-11)=0

Solution for (w-7)(2w-11)=0 equation:

(w-7)(2w-11)=0

We multiply parentheses ..

(+2w^2-11w-14w+77)=0

We get rid of parentheses

2w^2-11w-14w+77=0

We add all the numbers together, and all the variables

2w^2-25w+77=0

a = 2; b = -25; c = +77;
Δ = b2-4ac
Δ = -252-4·2·77
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-3}{2*2}=\frac{22}{4}
=5+1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+3}{2*2}=\frac{28}{4}
=7
$