0=w^2+5w-176

Solution for 0=w^2+5w-176 equation:

0=w^2+5w-176

We move all terms to the left:

0-(w^2+5w-176)=0

We add all the numbers together, and all the variables

-(w^2+5w-176)=0

We get rid of parentheses

-w^2-5w+176=0

We add all the numbers together, and all the variables

-1w^2-5w+176=0

a = -1; b = -5; c = +176;
Δ = b2-4ac
Δ = -52-4·(-1)·176
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-27}{2*-1}=\frac{-22}{-2}
=+11
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+27}{2*-1}=\frac{32}{-2}
=-16
$