2x-10/x=12

Solution for 2x-10/x=12 equation:

2x-10/x=12

We move all terms to the left:

2x-10/x-(12)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


2x*x-12*x-10=0

We add all the numbers together, and all the variables

-12x+2x*x-10=0

Wy multiply elements

2x^2-12x-10=0

a = 2; b = -12; c = -10;
Δ = b2-4ac
Δ = -122-4·2·(-10)
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{14}}{2*2}=\frac{12-4\sqrt{14}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{14}}{2*2}=\frac{12+4\sqrt{14}}{4}
$