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

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

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

We move all terms to the left:

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


Domain of the equation: 3x)+1)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

12x^2-30x=0

a = 12; b = -30; c = 0;
Δ = b2-4ac
Δ = -302-4·12·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-30}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+30}{2*12}=\frac{60}{24}
=2+1/2
$