2/x-3=2x-12

Solution for 2/x-3=2x-12 equation:

2/x-3=2x-12

We move all terms to the left:

2/x-3-(2x-12)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

2/x-2x+12-3=0

We multiply all the terms by the denominator


-2x*x+12*x-3*x+2=0

We add all the numbers together, and all the variables

9x-2x*x+2=0

Wy multiply elements

-2x^2+9x+2=0

a = -2; b = 9; c = +2;
Δ = b2-4ac
Δ = 92-4·(-2)·2
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{97}}{2*-2}=\frac{-9-\sqrt{97}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{97}}{2*-2}=\frac{-9+\sqrt{97}}{-4}
$