x-10=1/3x

Solution for x-10=1/3x equation:

x-10=1/3x

We move all terms to the left:

x-10-(1/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+1/3x)-10=0

We get rid of parentheses

x-1/3x-10=0

We multiply all the terms by the denominator


x*3x-10*3x-1=0

Wy multiply elements

3x^2-30x-1=0

a = 3; b = -30; c = -1;
Δ = b2-4ac
Δ = -302-4·3·(-1)
Δ = 912
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:

$\sqrt{\Delta}=\sqrt{912}=\sqrt{16*57}=\sqrt{16}*\sqrt{57}=4\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-4\sqrt{57}}{2*3}=\frac{30-4\sqrt{57}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+4\sqrt{57}}{2*3}=\frac{30+4\sqrt{57}}{6}
$