1/10*x=5-10x

Solution for 1/10*x=5-10x equation:

1/10x=5-10x

We move all terms to the left:

1/10x-(5-10x)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We add all the numbers together, and all the variables

1/10x-(-10x+5)=0

We get rid of parentheses

1/10x+10x-5=0

We multiply all the terms by the denominator


10x*10x-5*10x+1=0

Wy multiply elements

100x^2-50x+1=0

a = 100; b = -50; c = +1;
Δ = b2-4ac
Δ = -502-4·100·1
Δ = 2100
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:

$\sqrt{\Delta}=\sqrt{2100}=\sqrt{100*21}=\sqrt{100}*\sqrt{21}=10\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-10\sqrt{21}}{2*100}=\frac{50-10\sqrt{21}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+10\sqrt{21}}{2*100}=\frac{50+10\sqrt{21}}{200}
$