78/x=3x=

Solution for 78/x=3x= equation:

78/x=3x=

We move all terms to the left:

78/x-(3x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-3x+78/x=0

We multiply all the terms by the denominator


-3x*x+78=0

Wy multiply elements

-3x^2+78=0

a = -3; b = 0; c = +78;
Δ = b2-4ac
Δ = 02-4·(-3)·78
Δ = 936
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:

$\sqrt{\Delta}=\sqrt{936}=\sqrt{36*26}=\sqrt{36}*\sqrt{26}=6\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{26}}{2*-3}=\frac{0-6\sqrt{26}}{-6}
=-\frac{6\sqrt{26}}{-6}
=-\frac{\sqrt{26}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{26}}{2*-3}=\frac{0+6\sqrt{26}}{-6}
=\frac{6\sqrt{26}}{-6}
=\frac{\sqrt{26}}{-1}
$