2x-5/6x+8-10=0

Solution for 2x-5/6x+8-10=0 equation:

2x-5/6x+8-10=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

2x-5/6x-2=0

We multiply all the terms by the denominator


2x*6x-2*6x-5=0

Wy multiply elements

12x^2-12x-5=0

a = 12; b = -12; c = -5;
Δ = b2-4ac
Δ = -122-4·12·(-5)
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8\sqrt{6}}{2*12}=\frac{12-8\sqrt{6}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8\sqrt{6}}{2*12}=\frac{12+8\sqrt{6}}{24}
$