1/3x+4x=91

Solution for 1/3x+4x=91 equation:

1/3x+4x=91

We move all terms to the left:

1/3x+4x-(91)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

4x+1/3x-91=0

We multiply all the terms by the denominator


4x*3x-91*3x+1=0

Wy multiply elements

12x^2-273x+1=0

a = 12; b = -273; c = +1;
Δ = b2-4ac
Δ = -2732-4·12·1
Δ = 74481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-273)-\sqrt{74481}}{2*12}=\frac{273-\sqrt{74481}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-273)+\sqrt{74481}}{2*12}=\frac{273+\sqrt{74481}}{24}
$