9w=w^2+7

Solution for 9w=w^2+7 equation:

9w=w^2+7

We move all terms to the left:

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

We get rid of parentheses

-w^2+9w-7=0

We add all the numbers together, and all the variables

-1w^2+9w-7=0

a = -1; b = 9; c = -7;
Δ = b2-4ac
Δ = 92-4·(-1)·(-7)
Δ = 53
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{-(9)-\sqrt{53}}{2*-1}=\frac{-9-\sqrt{53}}{-2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{53}}{2*-1}=\frac{-9+\sqrt{53}}{-2}
$