179=x^2+x+24

Solution for 179=x^2+x+24 equation:

179=x^2+x+24

We move all terms to the left:

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

We get rid of parentheses

-x^2-x-24+179=0

We add all the numbers together, and all the variables

-1x^2-1x+155=0

a = -1; b = -1; c = +155;
Δ = b2-4ac
Δ = -12-4·(-1)·155
Δ = 621
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{621}=\sqrt{9*69}=\sqrt{9}*\sqrt{69}=3\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-3\sqrt{69}}{2*-1}=\frac{1-3\sqrt{69}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3\sqrt{69}}{2*-1}=\frac{1+3\sqrt{69}}{-2}
$