18x-x^2-79=0

Solution for 18x-x^2-79=0 equation:

18x-x^2-79=0

We add all the numbers together, and all the variables

-1x^2+18x-79=0

a = -1; b = 18; c = -79;
Δ = b2-4ac
Δ = 182-4·(-1)·(-79)
Δ = 8
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:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{2}}{2*-1}=\frac{-18-2\sqrt{2}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{2}}{2*-1}=\frac{-18+2\sqrt{2}}{-2}
$