80-x=1/4x

Solution for 80-x=1/4x equation:

80-x=1/4x

We move all terms to the left:

80-x-(1/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-x-(+1/4x)+80=0

We add all the numbers together, and all the variables

-1x-(+1/4x)+80=0

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-4x^2+320x-1=0

a = -4; b = 320; c = -1;
Δ = b2-4ac
Δ = 3202-4·(-4)·(-1)
Δ = 102384
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:

$\sqrt{\Delta}=\sqrt{102384}=\sqrt{1296*79}=\sqrt{1296}*\sqrt{79}=36\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(320)-36\sqrt{79}}{2*-4}=\frac{-320-36\sqrt{79}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(320)+36\sqrt{79}}{2*-4}=\frac{-320+36\sqrt{79}}{-8}
$