(1/3)x+x+3x=91

Solution for (1/3)x+x+3x=91 equation:

(1/3)x+x+3x=91

We move all terms to the left:

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


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses

x^2+4x-91=0

a = 1; b = 4; c = -91;
Δ = b2-4ac
Δ = 42-4·1·(-91)
Δ = 380
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:

$\sqrt{\Delta}=\sqrt{380}=\sqrt{4*95}=\sqrt{4}*\sqrt{95}=2\sqrt{95}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{95}}{2*1}=\frac{-4-2\sqrt{95}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{95}}{2*1}=\frac{-4+2\sqrt{95}}{2}
$