2x-3/3x-10=14

Solution for 2x-3/3x-10=14 equation:

2x-3/3x-10=14

We move all terms to the left:

2x-3/3x-10-(14)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2x-3/3x-24=0

We multiply all the terms by the denominator


2x*3x-24*3x-3=0

Wy multiply elements

6x^2-72x-3=0

a = 6; b = -72; c = -3;
Δ = b2-4ac
Δ = -722-4·6·(-3)
Δ = 5256
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:

$\sqrt{\Delta}=\sqrt{5256}=\sqrt{36*146}=\sqrt{36}*\sqrt{146}=6\sqrt{146}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-6\sqrt{146}}{2*6}=\frac{72-6\sqrt{146}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+6\sqrt{146}}{2*6}=\frac{72+6\sqrt{146}}{12}
$