9(w-9)-2=-7w(w-8)

Solution for 9(w-9)-2=-7w(w-8) equation:

9(w-9)-2=-7w(w-8)

We move all terms to the left:

9(w-9)-2-(-7w(w-8))=0

We multiply parentheses

9w-(-7w(w-8))-81-2=0


We calculate terms in parentheses: -(-7w(w-8)), so:

-7w(w-8)

We multiply parentheses

-7w^2+56w

Back to the equation:

-(-7w^2+56w)


We add all the numbers together, and all the variables

-(-7w^2+56w)+9w-83=0

We get rid of parentheses

7w^2-56w+9w-83=0

We add all the numbers together, and all the variables

7w^2-47w-83=0

a = 7; b = -47; c = -83;
Δ = b2-4ac
Δ = -472-4·7·(-83)
Δ = 4533
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-\sqrt{4533}}{2*7}=\frac{47-\sqrt{4533}}{14}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+\sqrt{4533}}{2*7}=\frac{47+\sqrt{4533}}{14}
$