92=X+1/3x

Solution for 92=X+1/3x equation:

92=X+1/3X

We move all terms to the left:

92-(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)+92=0

We get rid of parentheses

-X-1/3X+92=0

We multiply all the terms by the denominator


-X*3X+92*3X-1=0

Wy multiply elements

-3X^2+276X-1=0

a = -3; b = 276; c = -1;
Δ = b2-4ac
Δ = 2762-4·(-3)·(-1)
Δ = 76164
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:

$\sqrt{\Delta}=\sqrt{76164}=\sqrt{4*19041}=\sqrt{4}*\sqrt{19041}=2\sqrt{19041}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(276)-2\sqrt{19041}}{2*-3}=\frac{-276-2\sqrt{19041}}{-6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(276)+2\sqrt{19041}}{2*-3}=\frac{-276+2\sqrt{19041}}{-6}
$