80/2x=x-4

Solution for 80/2x=x-4 equation:

80/2x=x-4

We move all terms to the left:

80/2x-(x-4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

80/2x-x+4=0

We multiply all the terms by the denominator


-x*2x+4*2x+80=0

Wy multiply elements

-2x^2+8x+80=0

a = -2; b = 8; c = +80;
Δ = b2-4ac
Δ = 82-4·(-2)·80
Δ = 704
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:

$\sqrt{\Delta}=\sqrt{704}=\sqrt{64*11}=\sqrt{64}*\sqrt{11}=8\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{11}}{2*-2}=\frac{-8-8\sqrt{11}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{11}}{2*-2}=\frac{-8+8\sqrt{11}}{-4}
$