5/7x-5/14x=-15

Solution for 5/7x-5/14x=-15 equation:

5/7x-5/14x=-15

We move all terms to the left:

5/7x-5/14x-(-15)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 14x!=0

x!=0/14

x!=0

x∈R


We add all the numbers together, and all the variables

5/7x-5/14x+15=0

We calculate fractions


70x/98x^2+(-35x)/98x^2+15=0

We multiply all the terms by the denominator


70x+(-35x)+15*98x^2=0

Wy multiply elements

1470x^2+70x+(-35x)=0

We get rid of parentheses

1470x^2+70x-35x=0

We add all the numbers together, and all the variables

1470x^2+35x=0

a = 1470; b = 35; c = 0;
Δ = b2-4ac
Δ = 352-4·1470·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-35}{2*1470}=\frac{-70}{2940}
=-1/42
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+35}{2*1470}=\frac{0}{2940}
=0
$