3x=9/10x=

Solution for 3x=9/10x= equation:

3x=9/10x=

We move all terms to the left:

3x-(9/10x)=0


Domain of the equation: 10x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x-(+9/10x)=0

We get rid of parentheses

3x-9/10x=0

We multiply all the terms by the denominator


3x*10x-9=0

Wy multiply elements

30x^2-9=0

a = 30; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·30·(-9)
Δ = 1080
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:

$\sqrt{\Delta}=\sqrt{1080}=\sqrt{36*30}=\sqrt{36}*\sqrt{30}=6\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{30}}{2*30}=\frac{0-6\sqrt{30}}{60}
=-\frac{6\sqrt{30}}{60}
=-\frac{\sqrt{30}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{30}}{2*30}=\frac{0+6\sqrt{30}}{60}
=\frac{6\sqrt{30}}{60}
=\frac{\sqrt{30}}{10}
$