57x-2-6/7x=-13

Solution for 57x-2-6/7x=-13 equation:

57x-2-6/7x=-13

We move all terms to the left:

57x-2-6/7x-(-13)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

57x-6/7x+11=0

We multiply all the terms by the denominator


57x*7x+11*7x-6=0

Wy multiply elements

399x^2+77x-6=0

a = 399; b = 77; c = -6;
Δ = b2-4ac
Δ = 772-4·399·(-6)
Δ = 15505
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(77)-\sqrt{15505}}{2*399}=\frac{-77-\sqrt{15505}}{798}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(77)+\sqrt{15505}}{2*399}=\frac{-77+\sqrt{15505}}{798}
$