x+2=3/10x

Solution for x+2=3/10x equation:

x+2=3/10x

We move all terms to the left:

x+2-(3/10x)=0


Domain of the equation: 10x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+3/10x)+2=0

We get rid of parentheses

x-3/10x+2=0

We multiply all the terms by the denominator


x*10x+2*10x-3=0

Wy multiply elements

10x^2+20x-3=0

a = 10; b = 20; c = -3;
Δ = b2-4ac
Δ = 202-4·10·(-3)
Δ = 520
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:

$\sqrt{\Delta}=\sqrt{520}=\sqrt{4*130}=\sqrt{4}*\sqrt{130}=2\sqrt{130}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{130}}{2*10}=\frac{-20-2\sqrt{130}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{130}}{2*10}=\frac{-20+2\sqrt{130}}{20}
$