6x-15/x=13

Solution for 6x-15/x=13 equation:

6x-15/x=13

We move all terms to the left:

6x-15/x-(13)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


6x*x-13*x-15=0

We add all the numbers together, and all the variables

-13x+6x*x-15=0

Wy multiply elements

6x^2-13x-15=0

a = 6; b = -13; c = -15;
Δ = b2-4ac
Δ = -132-4·6·(-15)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-23}{2*6}=\frac{-10}{12}
=-5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+23}{2*6}=\frac{36}{12}
=3
$