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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

-1x+(-2x+60)(-2x+80)=0

We multiply parentheses ..

(+4x^2-160x-120x+4800)-1x=0

We get rid of parentheses

4x^2-160x-120x-1x+4800=0

We add all the numbers together, and all the variables

4x^2-281x+4800=0

a = 4; b = -281; c = +4800;
Δ = b2-4ac
Δ = -2812-4·4·4800
Δ = 2161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-281)-\sqrt{2161}}{2*4}=\frac{281-\sqrt{2161}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-281)+\sqrt{2161}}{2*4}=\frac{281+\sqrt{2161}}{8}
$