(3/5)x-21=x/10

Solution for (3/5)x-21=x/10 equation:

(3/5)x-21=x/10

We move all terms to the left:

(3/5)x-21-(x/10)=0


Domain of the equation: 5)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+3/5)x-(+x/10)-21=0

We multiply parentheses

3x^2-(+x/10)-21=0

We get rid of parentheses

3x^2-x/10-21=0

We multiply all the terms by the denominator


3x^2*10-x-21*10=0

We add all the numbers together, and all the variables

3x^2*10-1x-210=0

Wy multiply elements

30x^2-1x-210=0

a = 30; b = -1; c = -210;
Δ = b2-4ac
Δ = -12-4·30·(-210)
Δ = 25201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{25201}}{2*30}=\frac{1-\sqrt{25201}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{25201}}{2*30}=\frac{1+\sqrt{25201}}{60}
$