144-6x=x(24-x)

Solution for 144-6x=x(24-x) equation:

144-6x=x(24-x)

We move all terms to the left:

144-6x-(x(24-x))=0

We add all the numbers together, and all the variables

-6x-(x(-1x+24))+144=0


We calculate terms in parentheses: -(x(-1x+24)), so:

x(-1x+24)

We multiply parentheses

-1x^2+24x

Back to the equation:

-(-1x^2+24x)


We get rid of parentheses

1x^2-24x-6x+144=0

We add all the numbers together, and all the variables

x^2-30x+144=0

a = 1; b = -30; c = +144;
Δ = b2-4ac
Δ = -302-4·1·144
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-18}{2*1}=\frac{12}{2}
=6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+18}{2*1}=\frac{48}{2}
=24
$