12=2x-3/x-4

Solution for 12=2x-3/x-4 equation:

12=2x-3/x-4

We move all terms to the left:

12-(2x-3/x-4)=0


Domain of the equation: x-4)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

16x-2x*x+3=0

Wy multiply elements

-2x^2+16x+3=0

a = -2; b = 16; c = +3;
Δ = b2-4ac
Δ = 162-4·(-2)·3
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{70}}{2*-2}=\frac{-16-2\sqrt{70}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{70}}{2*-2}=\frac{-16+2\sqrt{70}}{-4}
$