39/x=13;x=4

Solution for 39/x=13;x=4 equation:

39/x=13x=4

We move all terms to the left:

39/x-(13x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-13x+39/x=0

We multiply all the terms by the denominator


-13x*x+39=0

Wy multiply elements

-13x^2+39=0

a = -13; b = 0; c = +39;
Δ = b2-4ac
Δ = 02-4·(-13)·39
Δ = 2028
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:

$\sqrt{\Delta}=\sqrt{2028}=\sqrt{676*3}=\sqrt{676}*\sqrt{3}=26\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-26\sqrt{3}}{2*-13}=\frac{0-26\sqrt{3}}{-26}
=-\frac{26\sqrt{3}}{-26}
=-\frac{\sqrt{3}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+26\sqrt{3}}{2*-13}=\frac{0+26\sqrt{3}}{-26}
=\frac{26\sqrt{3}}{-26}
=\frac{\sqrt{3}}{-1}
$