18x(10-x)=54

Solution for 18x(10-x)=54 equation:

18x(10-x)=54

We move all terms to the left:

18x(10-x)-(54)=0

We add all the numbers together, and all the variables

18x(-1x+10)-54=0

We multiply parentheses

-18x^2+180x-54=0

a = -18; b = 180; c = -54;
Δ = b2-4ac
Δ = 1802-4·(-18)·(-54)
Δ = 28512
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:

$\sqrt{\Delta}=\sqrt{28512}=\sqrt{1296*22}=\sqrt{1296}*\sqrt{22}=36\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-36\sqrt{22}}{2*-18}=\frac{-180-36\sqrt{22}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+36\sqrt{22}}{2*-18}=\frac{-180+36\sqrt{22}}{-36}
$