3x+4/5x+4=48

Solution for 3x+4/5x+4=48 equation:

3x+4/5x+4=48

We move all terms to the left:

3x+4/5x+4-(48)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

3x+4/5x-44=0

We multiply all the terms by the denominator


3x*5x-44*5x+4=0

Wy multiply elements

15x^2-220x+4=0

a = 15; b = -220; c = +4;
Δ = b2-4ac
Δ = -2202-4·15·4
Δ = 48160
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:

$\sqrt{\Delta}=\sqrt{48160}=\sqrt{16*3010}=\sqrt{16}*\sqrt{3010}=4\sqrt{3010}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-220)-4\sqrt{3010}}{2*15}=\frac{220-4\sqrt{3010}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-220)+4\sqrt{3010}}{2*15}=\frac{220+4\sqrt{3010}}{30}
$