0=w^2+7w-144

Solution for 0=w^2+7w-144 equation:

0=w^2+7w-144

We move all terms to the left:

0-(w^2+7w-144)=0

We add all the numbers together, and all the variables

-(w^2+7w-144)=0

We get rid of parentheses

-w^2-7w+144=0

We add all the numbers together, and all the variables

-1w^2-7w+144=0

a = -1; b = -7; c = +144;
Δ = b2-4ac
Δ = -72-4·(-1)·144
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-25}{2*-1}=\frac{-18}{-2}
=+9
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+25}{2*-1}=\frac{32}{-2}
=-16
$