5/77x-2-6/7x=-13

Solution for 5/77x-2-6/7x=-13 equation:

5/77x-2-6/7x=-13

We move all terms to the left:

5/77x-2-6/7x-(-13)=0


Domain of the equation: 77x!=0

x!=0/77

x!=0

x∈R



Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

5/77x-6/7x+11=0

We calculate fractions


35x/539x^2+(-462x)/539x^2+11=0

We multiply all the terms by the denominator


35x+(-462x)+11*539x^2=0

Wy multiply elements

5929x^2+35x+(-462x)=0

We get rid of parentheses

5929x^2+35x-462x=0

We add all the numbers together, and all the variables

5929x^2-427x=0

a = 5929; b = -427; c = 0;
Δ = b2-4ac
Δ = -4272-4·5929·0
Δ = 182329
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{182329}=427$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-427)-427}{2*5929}=\frac{0}{11858}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-427)+427}{2*5929}=\frac{854}{11858}
=61/847
$