156/x=13x-54

Solution for 156/x=13x-54 equation:

156/x=13x-54

We move all terms to the left:

156/x-(13x-54)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

156/x-13x+54=0

We multiply all the terms by the denominator


-13x*x+54*x+156=0

We add all the numbers together, and all the variables

54x-13x*x+156=0

Wy multiply elements

-13x^2+54x+156=0

a = -13; b = 54; c = +156;
Δ = b2-4ac
Δ = 542-4·(-13)·156
Δ = 11028
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:

$\sqrt{\Delta}=\sqrt{11028}=\sqrt{4*2757}=\sqrt{4}*\sqrt{2757}=2\sqrt{2757}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-2\sqrt{2757}}{2*-13}=\frac{-54-2\sqrt{2757}}{-26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+2\sqrt{2757}}{2*-13}=\frac{-54+2\sqrt{2757}}{-26}
$