(24-x)(10-x)=120

Solution for (24-x)(10-x)=120 equation:

(24-x)(10-x)=120

We move all terms to the left:

(24-x)(10-x)-(120)=0

We add all the numbers together, and all the variables

(-1x+24)(-1x+10)-120=0

We multiply parentheses ..

(+x^2-10x-24x+240)-120=0

We get rid of parentheses

x^2-10x-24x+240-120=0

We add all the numbers together, and all the variables

x^2-34x+120=0

a = 1; b = -34; c = +120;
Δ = b2-4ac
Δ = -342-4·1·120
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-26}{2*1}=\frac{8}{2}
=4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+26}{2*1}=\frac{60}{2}
=30
$