98=2x+1/3x

Solution for 98=2x+1/3x equation:

98=2x+1/3x

We move all terms to the left:

98-(2x+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

-(+2x+1/3x)+98=0

We get rid of parentheses

-2x-1/3x+98=0

We multiply all the terms by the denominator


-2x*3x+98*3x-1=0

Wy multiply elements

-6x^2+294x-1=0

a = -6; b = 294; c = -1;
Δ = b2-4ac
Δ = 2942-4·(-6)·(-1)
Δ = 86412
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:

$\sqrt{\Delta}=\sqrt{86412}=\sqrt{4*21603}=\sqrt{4}*\sqrt{21603}=2\sqrt{21603}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(294)-2\sqrt{21603}}{2*-6}=\frac{-294-2\sqrt{21603}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(294)+2\sqrt{21603}}{2*-6}=\frac{-294+2\sqrt{21603}}{-12}
$