9w2=18w+7

Solution for 9w2=18w+7 equation:

9w^2=18w+7

We move all terms to the left:

9w^2-(18w+7)=0

We get rid of parentheses

9w^2-18w-7=0

a = 9; b = -18; c = -7;
Δ = b2-4ac
Δ = -182-4·9·(-7)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-24}{2*9}=\frac{-6}{18}
=-1/3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+24}{2*9}=\frac{42}{18}
=2+1/3
$