X/x+5=2x-12/2x-4

Solution for X/x+5=2x-12/2x-4 equation:

X/X+5=2X-12/2X-4

We move all terms to the left:

X/X+5-(2X-12/2X-4)=0


Domain of the equation: X!=0

X∈R



Domain of the equation: 2X-4)!=0

X∈R


We get rid of parentheses

X/X-2X+12/2X+4+5=0

Fractions to decimals

12/2X-2X+4+5+1=0

We multiply all the terms by the denominator


-2X*2X+4*2X+5*2X+1*2X+12=0

Wy multiply elements

-4X^2+8X+10X+2X+12=0

We add all the numbers together, and all the variables

-4X^2+20X+12=0

a = -4; b = 20; c = +12;
Δ = b2-4ac
Δ = 202-4·(-4)·12
Δ = 592
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:

$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{37}}{2*-4}=\frac{-20-4\sqrt{37}}{-8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{37}}{2*-4}=\frac{-20+4\sqrt{37}}{-8}
$