-18w+9=9(-w2+1)

Solution for -18w+9=9(-w2+1) equation:

-18w+9=9(-w2+1)

We move all terms to the left:

-18w+9-(9(-w2+1))=0

We add all the numbers together, and all the variables

-(9(-1w^2+1))-18w+9=0


We calculate terms in parentheses: -(9(-1w^2+1)), so:

9(-1w^2+1)

We multiply parentheses

-9w^2+9

Back to the equation:

-(-9w^2+9)


We get rid of parentheses

9w^2-18w-9+9=0

We add all the numbers together, and all the variables

9w^2-18w=0

a = 9; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·9·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*9}=\frac{0}{18}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*9}=\frac{36}{18}
=2
$