6.75x=131/2x

Solution for 6.75x=131/2x equation:

6.75x=131/2x

We move all terms to the left:

6.75x-(131/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

6.75x-(+131/2x)=0

We get rid of parentheses

6.75x-131/2x=0

We multiply all the terms by the denominator


(6.75x)*2x-131=0

We add all the numbers together, and all the variables

(+6.75x)*2x-131=0

We multiply parentheses

12x^2-131=0

a = 12; b = 0; c = -131;
Δ = b2-4ac
Δ = 02-4·12·(-131)
Δ = 6288
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:

$\sqrt{\Delta}=\sqrt{6288}=\sqrt{16*393}=\sqrt{16}*\sqrt{393}=4\sqrt{393}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{393}}{2*12}=\frac{0-4\sqrt{393}}{24}
=-\frac{4\sqrt{393}}{24}
=-\frac{\sqrt{393}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{393}}{2*12}=\frac{0+4\sqrt{393}}{24}
=\frac{4\sqrt{393}}{24}
=\frac{\sqrt{393}}{6}
$