1/5x+3x=96

Solution for 1/5x+3x=96 equation:

1/5x+3x=96

We move all terms to the left:

1/5x+3x-(96)=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+1/5x-96=0

We multiply all the terms by the denominator


3x*5x-96*5x+1=0

Wy multiply elements

15x^2-480x+1=0

a = 15; b = -480; c = +1;
Δ = b2-4ac
Δ = -4802-4·15·1
Δ = 230340
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:

$\sqrt{\Delta}=\sqrt{230340}=\sqrt{4*57585}=\sqrt{4}*\sqrt{57585}=2\sqrt{57585}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-480)-2\sqrt{57585}}{2*15}=\frac{480-2\sqrt{57585}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-480)+2\sqrt{57585}}{2*15}=\frac{480+2\sqrt{57585}}{30}
$