(50-2x)(120-2x)=3000

Solution for (50-2x)(120-2x)=3000 equation:

(50-2x)(120-2x)=3000

We move all terms to the left:

(50-2x)(120-2x)-(3000)=0

We add all the numbers together, and all the variables

(-2x+50)(-2x+120)-3000=0

We multiply parentheses ..

(+4x^2-240x-100x+6000)-3000=0

We get rid of parentheses

4x^2-240x-100x+6000-3000=0

We add all the numbers together, and all the variables

4x^2-340x+3000=0

a = 4; b = -340; c = +3000;
Δ = b2-4ac
Δ = -3402-4·4·3000
Δ = 67600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{67600}=260$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-340)-260}{2*4}=\frac{80}{8}
=10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-340)+260}{2*4}=\frac{600}{8}
=75
$