120=x(23-x)

Solution for 120=x(23-x) equation:

120=x(23-x)

We move all terms to the left:

120-(x(23-x))=0

We add all the numbers together, and all the variables

-(x(-1x+23))+120=0


We calculate terms in parentheses: -(x(-1x+23)), so:

x(-1x+23)

We multiply parentheses

-1x^2+23x

Back to the equation:

-(-1x^2+23x)


We get rid of parentheses

1x^2-23x+120=0

We add all the numbers together, and all the variables

x^2-23x+120=0

a = 1; b = -23; c = +120;
Δ = b2-4ac
Δ = -232-4·1·120
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-7}{2*1}=\frac{16}{2}
=8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+7}{2*1}=\frac{30}{2}
=15
$