4/5x-4/7x=4

Solution for 4/5x-4/7x=4 equation:

4/5x-4/7x=4

We move all terms to the left:

4/5x-4/7x-(4)=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 calculate fractions


28x/35x^2+(-20x)/35x^2-4=0

We multiply all the terms by the denominator


28x+(-20x)-4*35x^2=0

Wy multiply elements

-140x^2+28x+(-20x)=0

We get rid of parentheses

-140x^2+28x-20x=0

We add all the numbers together, and all the variables

-140x^2+8x=0

a = -140; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-140)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-140}=\frac{-16}{-280}
=2/35
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-140}=\frac{0}{-280}
=0
$