w^2-9w=-17

Solution for w^2-9w=-17 equation:

w^2-9w=-17

We move all terms to the left:

w^2-9w-(-17)=0

We add all the numbers together, and all the variables

w^2-9w+17=0

a = 1; b = -9; c = +17;
Δ = b2-4ac
Δ = -92-4·1·17
Δ = 13
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{13}}{2*1}=\frac{9-\sqrt{13}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{13}}{2*1}=\frac{9+\sqrt{13}}{2}
$