160-x=1/4x

Solution for 160-x=1/4x equation:

160-x=1/4x

We move all terms to the left:

160-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)+160=0

We add all the numbers together, and all the variables

-1x-(+1/4x)+160=0

We get rid of parentheses

-1x-1/4x+160=0

We multiply all the terms by the denominator


-1x*4x+160*4x-1=0

Wy multiply elements

-4x^2+640x-1=0

a = -4; b = 640; c = -1;
Δ = b2-4ac
Δ = 6402-4·(-4)·(-1)
Δ = 409584
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:

$\sqrt{\Delta}=\sqrt{409584}=\sqrt{16*25599}=\sqrt{16}*\sqrt{25599}=4\sqrt{25599}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(640)-4\sqrt{25599}}{2*-4}=\frac{-640-4\sqrt{25599}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(640)+4\sqrt{25599}}{2*-4}=\frac{-640+4\sqrt{25599}}{-8}
$