4x-10/3x+1=1

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

4x-10/3x+1=1

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

4x-10/3x=0

We multiply all the terms by the denominator


4x*3x-10=0

Wy multiply elements

12x^2-10=0

a = 12; b = 0; c = -10;
Δ = b2-4ac
Δ = 02-4·12·(-10)
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{30}}{2*12}=\frac{0-4\sqrt{30}}{24}
=-\frac{4\sqrt{30}}{24}
=-\frac{\sqrt{30}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{30}}{2*12}=\frac{0+4\sqrt{30}}{24}
=\frac{4\sqrt{30}}{24}
=\frac{\sqrt{30}}{6}
$