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 get rid of parentheses

x-1/5x+12=0

We multiply all the terms by the denominator


x*5x+12*5x-1=0

Wy multiply elements

5x^2+60x-1=0

a = 5; b = 60; c = -1;
Δ = b2-4ac
Δ = 602-4·5·(-1)
Δ = 3620
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:

$\sqrt{\Delta}=\sqrt{3620}=\sqrt{4*905}=\sqrt{4}*\sqrt{905}=2\sqrt{905}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-2\sqrt{905}}{2*5}=\frac{-60-2\sqrt{905}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+2\sqrt{905}}{2*5}=\frac{-60+2\sqrt{905}}{10}
$