5=x(18-x)

Solution for 5=x(18-x) equation:

5=x(18-x)

We move all terms to the left:

5-(x(18-x))=0

We add all the numbers together, and all the variables

-(x(-1x+18))+5=0


We calculate terms in parentheses: -(x(-1x+18)), so:

x(-1x+18)

We multiply parentheses

-1x^2+18x

Back to the equation:

-(-1x^2+18x)


We get rid of parentheses

1x^2-18x+5=0

We add all the numbers together, and all the variables

x^2-18x+5=0

a = 1; b = -18; c = +5;
Δ = b2-4ac
Δ = -182-4·1·5
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-4\sqrt{19}}{2*1}=\frac{18-4\sqrt{19}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+4\sqrt{19}}{2*1}=\frac{18+4\sqrt{19}}{2}
$