4/5x-x=80

Solution for 4/5x-x=80 equation:

4/5x-x=80

We move all terms to the left:

4/5x-x-(80)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+4/5x-80=0

We multiply all the terms by the denominator


-1x*5x-80*5x+4=0

Wy multiply elements

-5x^2-400x+4=0

a = -5; b = -400; c = +4;
Δ = b2-4ac
Δ = -4002-4·(-5)·4
Δ = 160080
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:

$\sqrt{\Delta}=\sqrt{160080}=\sqrt{16*10005}=\sqrt{16}*\sqrt{10005}=4\sqrt{10005}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-400)-4\sqrt{10005}}{2*-5}=\frac{400-4\sqrt{10005}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-400)+4\sqrt{10005}}{2*-5}=\frac{400+4\sqrt{10005}}{-10}
$