3x-12/x=15-4x-3

Solution for 3x-12/x=15-4x-3 equation:

3x-12/x=15-4x-3

We move all terms to the left:

3x-12/x-(15-4x-3)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

3x-12/x-(-4x+12)=0

We get rid of parentheses

3x-12/x+4x-12=0

We multiply all the terms by the denominator


3x*x+4x*x-12*x-12=0

We add all the numbers together, and all the variables

-12x+3x*x+4x*x-12=0

Wy multiply elements

3x^2+4x^2-12x-12=0

We add all the numbers together, and all the variables

7x^2-12x-12=0

a = 7; b = -12; c = -12;
Δ = b2-4ac
Δ = -122-4·7·(-12)
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{30}}{2*7}=\frac{12-4\sqrt{30}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{30}}{2*7}=\frac{12+4\sqrt{30}}{14}
$