79=24x+x^2

Solution for 79=24x+x^2 equation:

79=24x+x^2

We move all terms to the left:

79-(24x+x^2)=0

We get rid of parentheses

-x^2-24x+79=0

We add all the numbers together, and all the variables

-1x^2-24x+79=0

a = -1; b = -24; c = +79;
Δ = b2-4ac
Δ = -242-4·(-1)·79
Δ = 892
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:

$\sqrt{\Delta}=\sqrt{892}=\sqrt{4*223}=\sqrt{4}*\sqrt{223}=2\sqrt{223}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{223}}{2*-1}=\frac{24-2\sqrt{223}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{223}}{2*-1}=\frac{24+2\sqrt{223}}{-2}
$