-26/13.x=15-17.x-7

Solution for -26/13.x=15-17.x-7 equation:

-26/13.x=15-17.x-7

We move all terms to the left:

-26/13.x-(15-17.x-7)=0


Domain of the equation: 13.x!=0

x!=0/13.

x!=0

x∈R


We add all the numbers together, and all the variables

-26/13.x-(-17x+8)=0

We get rid of parentheses

-26/13.x+17x-8=0

We multiply all the terms by the denominator


17x*13.x-8*13.x-26=0

Wy multiply elements

221x^2-104x-26=0

a = 221; b = -104; c = -26;
Δ = b2-4ac
Δ = -1042-4·221·(-26)
Δ = 33800
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:

$\sqrt{\Delta}=\sqrt{33800}=\sqrt{16900*2}=\sqrt{16900}*\sqrt{2}=130\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-104)-130\sqrt{2}}{2*221}=\frac{104-130\sqrt{2}}{442}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-104)+130\sqrt{2}}{2*221}=\frac{104+130\sqrt{2}}{442}
$