9(w-8)(w+5)=14

Solution for 9(w-8)(w+5)=14 equation:

9(w-8)(w+5)=14

We move all terms to the left:

9(w-8)(w+5)-(14)=0

We multiply parentheses ..

9(+w^2+5w-8w-40)-14=0

We multiply parentheses

9w^2+45w-72w-360-14=0

We add all the numbers together, and all the variables

9w^2-27w-374=0

a = 9; b = -27; c = -374;
Δ = b2-4ac
Δ = -272-4·9·(-374)
Δ = 14193
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{14193}=\sqrt{9*1577}=\sqrt{9}*\sqrt{1577}=3\sqrt{1577}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3\sqrt{1577}}{2*9}=\frac{27-3\sqrt{1577}}{18}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3\sqrt{1577}}{2*9}=\frac{27+3\sqrt{1577}}{18}
$