3x-10/x-6=0

Solution for 3x-10/x-6=0 equation:

3x-10/x-6=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


3x*x-6*x-10=0

We add all the numbers together, and all the variables

-6x+3x*x-10=0

Wy multiply elements

3x^2-6x-10=0

a = 3; b = -6; c = -10;
Δ = b2-4ac
Δ = -62-4·3·(-10)
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{39}}{2*3}=\frac{6-2\sqrt{39}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{39}}{2*3}=\frac{6+2\sqrt{39}}{6}
$