179.99999999999=x^2+x+24

Solution for 179.99999999999=x^2+x+24 equation:

179.99999999999=x^2+x+24

We move all terms to the left:

179.99999999999-(x^2+x+24)=0

We add all the numbers together, and all the variables

-(x^2+x+24)+180=0

We get rid of parentheses

-x^2-x-24+180=0

We add all the numbers together, and all the variables

-1x^2-1x+156=0

a = -1; b = -1; c = +156;
Δ = b2-4ac
Δ = -12-4·(-1)·156
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-25}{2*-1}=\frac{-24}{-2}
=+12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+25}{2*-1}=\frac{26}{-2}
=-13
$