7/5x-5/7x-6=10

Solution for 7/5x-5/7x-6=10 equation:

7/5x-5/7x-6=10

We move all terms to the left:

7/5x-5/7x-6-(10)=0


Domain of the equation: 5x!=0

x!=0/5

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

7/5x-5/7x-16=0

We calculate fractions


49x/35x^2+(-25x)/35x^2-16=0

We multiply all the terms by the denominator


49x+(-25x)-16*35x^2=0

Wy multiply elements

-560x^2+49x+(-25x)=0

We get rid of parentheses

-560x^2+49x-25x=0

We add all the numbers together, and all the variables

-560x^2+24x=0

a = -560; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·(-560)·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*-560}=\frac{-48}{-1120}
=3/70
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*-560}=\frac{0}{-1120}
=0
$