48/x=6x=8

Solution for 48/x=6x=8 equation:

48/x=6x=8

We move all terms to the left:

48/x-(6x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-6x+48/x=0

We multiply all the terms by the denominator


-6x*x+48=0

Wy multiply elements

-6x^2+48=0

a = -6; b = 0; c = +48;
Δ = b2-4ac
Δ = 02-4·(-6)·48
Δ = 1152
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:

$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{2}}{2*-6}=\frac{0-24\sqrt{2}}{-12}
=-\frac{24\sqrt{2}}{-12}
=-\frac{2\sqrt{2}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{2}}{2*-6}=\frac{0+24\sqrt{2}}{-12}
=\frac{24\sqrt{2}}{-12}
=\frac{2\sqrt{2}}{-1}
$