3000=(-2x+100)(-2x+60)

Solution for 3000=(-2x+100)(-2x+60) equation:

3000=(-2x+100)(-2x+60)

We move all terms to the left:

3000-((-2x+100)(-2x+60))=0

We multiply parentheses ..

-((+4x^2-120x-200x+6000))+3000=0


We calculate terms in parentheses: -((+4x^2-120x-200x+6000)), so:

(+4x^2-120x-200x+6000)

We get rid of parentheses

4x^2-120x-200x+6000

We add all the numbers together, and all the variables

4x^2-320x+6000

Back to the equation:

-(4x^2-320x+6000)


We get rid of parentheses

-4x^2+320x-6000+3000=0

We add all the numbers together, and all the variables

-4x^2+320x-3000=0

a = -4; b = 320; c = -3000;
Δ = b2-4ac
Δ = 3202-4·(-4)·(-3000)
Δ = 54400
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:

$\sqrt{\Delta}=\sqrt{54400}=\sqrt{1600*34}=\sqrt{1600}*\sqrt{34}=40\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(320)-40\sqrt{34}}{2*-4}=\frac{-320-40\sqrt{34}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(320)+40\sqrt{34}}{2*-4}=\frac{-320+40\sqrt{34}}{-8}
$