1000=(80-2x)(60-2x)

Solution for 1000=(80-2x)(60-2x) equation:

1000=(80-2x)(60-2x)

We move all terms to the left:

1000-((80-2x)(60-2x))=0

We add all the numbers together, and all the variables

-((-2x+80)(-2x+60))+1000=0

We multiply parentheses ..

-((+4x^2-120x-160x+4800))+1000=0


We calculate terms in parentheses: -((+4x^2-120x-160x+4800)), so:

(+4x^2-120x-160x+4800)

We get rid of parentheses

4x^2-120x-160x+4800

We add all the numbers together, and all the variables

4x^2-280x+4800

Back to the equation:

-(4x^2-280x+4800)


We get rid of parentheses

-4x^2+280x-4800+1000=0

We add all the numbers together, and all the variables

-4x^2+280x-3800=0

a = -4; b = 280; c = -3800;
Δ = b2-4ac
Δ = 2802-4·(-4)·(-3800)
Δ = 17600
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:

$\sqrt{\Delta}=\sqrt{17600}=\sqrt{1600*11}=\sqrt{1600}*\sqrt{11}=40\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(280)-40\sqrt{11}}{2*-4}=\frac{-280-40\sqrt{11}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(280)+40\sqrt{11}}{2*-4}=\frac{-280+40\sqrt{11}}{-8}
$