7x+6x=15/x

Solution for 7x+6x=15/x equation:

7x+6x=15/x

We move all terms to the left:

7x+6x-(15/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

7x+6x-(+15/x)=0

We add all the numbers together, and all the variables

13x-(+15/x)=0

We get rid of parentheses

13x-15/x=0

We multiply all the terms by the denominator


13x*x-15=0

Wy multiply elements

13x^2-15=0

a = 13; b = 0; c = -15;
Δ = b2-4ac
Δ = 02-4·13·(-15)
Δ = 780
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:

$\sqrt{\Delta}=\sqrt{780}=\sqrt{4*195}=\sqrt{4}*\sqrt{195}=2\sqrt{195}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{195}}{2*13}=\frac{0-2\sqrt{195}}{26}
=-\frac{2\sqrt{195}}{26}
=-\frac{\sqrt{195}}{13}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{195}}{2*13}=\frac{0+2\sqrt{195}}{26}
=\frac{2\sqrt{195}}{26}
=\frac{\sqrt{195}}{13}
$