4x-10=1/3x

Solution for 4x-10=1/3x equation:

4x-10=1/3x

We move all terms to the left:

4x-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

4x-(+1/3x)-10=0

We get rid of parentheses

4x-1/3x-10=0

We multiply all the terms by the denominator


4x*3x-10*3x-1=0

Wy multiply elements

12x^2-30x-1=0

a = 12; b = -30; c = -1;
Δ = b2-4ac
Δ = -302-4·12·(-1)
Δ = 948
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:

$\sqrt{\Delta}=\sqrt{948}=\sqrt{4*237}=\sqrt{4}*\sqrt{237}=2\sqrt{237}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{237}}{2*12}=\frac{30-2\sqrt{237}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{237}}{2*12}=\frac{30+2\sqrt{237}}{24}
$