(2w-7)(9-w)=0

Solution for (2w-7)(9-w)=0 equation:

(2w-7)(9-w)=0

We add all the numbers together, and all the variables

(2w-7)(-1w+9)=0

We multiply parentheses ..

(-2w^2+18w+7w-63)=0

We get rid of parentheses

-2w^2+18w+7w-63=0

We add all the numbers together, and all the variables

-2w^2+25w-63=0

a = -2; b = 25; c = -63;
Δ = b2-4ac
Δ = 252-4·(-2)·(-63)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-11}{2*-2}=\frac{-36}{-4}
=+9
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+11}{2*-2}=\frac{-14}{-4}
=3+1/2
$