6x-24/4x+72=48

Solution for 6x-24/4x+72=48 equation:

6x-24/4x+72=48

We move all terms to the left:

6x-24/4x+72-(48)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

6x-24/4x+24=0

We multiply all the terms by the denominator


6x*4x+24*4x-24=0

Wy multiply elements

24x^2+96x-24=0

a = 24; b = 96; c = -24;
Δ = b2-4ac
Δ = 962-4·24·(-24)
Δ = 11520
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:

$\sqrt{\Delta}=\sqrt{11520}=\sqrt{2304*5}=\sqrt{2304}*\sqrt{5}=48\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-48\sqrt{5}}{2*24}=\frac{-96-48\sqrt{5}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+48\sqrt{5}}{2*24}=\frac{-96+48\sqrt{5}}{48}
$