X+-12=1/5x

Solution for X+-12=1/5x equation:

X+-12=1/5X

We move all terms to the left:

X+-12-(1/5X)=0


Domain of the equation: 5X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-(+1/5X)-12+=0

We add all the numbers together, and all the variables

X-(+1/5X)=0

We get rid of parentheses

X-1/5X=0

We multiply all the terms by the denominator


X*5X-1=0

Wy multiply elements

5X^2-1=0

a = 5; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·5·(-1)
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{5}}{2*5}=\frac{0-2\sqrt{5}}{10}
=-\frac{2\sqrt{5}}{10}
=-\frac{\sqrt{5}}{5}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{5}}{2*5}=\frac{0+2\sqrt{5}}{10}
=\frac{2\sqrt{5}}{10}
=\frac{\sqrt{5}}{5}
$