12/5x-4=x+4

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

12/5x-4=x+4

We move all terms to the left:

12/5x-4-(x+4)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

12/5x-x-4-4=0

We multiply all the terms by the denominator


-x*5x-4*5x-4*5x+12=0

Wy multiply elements

-5x^2-20x-20x+12=0

We add all the numbers together, and all the variables

-5x^2-40x+12=0

a = -5; b = -40; c = +12;
Δ = b2-4ac
Δ = -402-4·(-5)·12
Δ = 1840
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:

$\sqrt{\Delta}=\sqrt{1840}=\sqrt{16*115}=\sqrt{16}*\sqrt{115}=4\sqrt{115}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{115}}{2*-5}=\frac{40-4\sqrt{115}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{115}}{2*-5}=\frac{40+4\sqrt{115}}{-10}
$