76=x+1/3x

Solution for 76=x+1/3x equation:

76=x+1/3x

We move all terms to the left:

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


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+x+1/3x)+76=0

We get rid of parentheses

-x-1/3x+76=0

We multiply all the terms by the denominator


-x*3x+76*3x-1=0

Wy multiply elements

-3x^2+228x-1=0

a = -3; b = 228; c = -1;
Δ = b2-4ac
Δ = 2282-4·(-3)·(-1)
Δ = 51972
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:

$\sqrt{\Delta}=\sqrt{51972}=\sqrt{4*12993}=\sqrt{4}*\sqrt{12993}=2\sqrt{12993}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(228)-2\sqrt{12993}}{2*-3}=\frac{-228-2\sqrt{12993}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(228)+2\sqrt{12993}}{2*-3}=\frac{-228+2\sqrt{12993}}{-6}
$