4/2x+6=10/7x-2

Solution for 4/2x+6=10/7x-2 equation:

4/2x+6=10/7x-2

We move all terms to the left:

4/2x+6-(10/7x-2)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 7x-2)!=0

x∈R


We get rid of parentheses

4/2x-10/7x+2+6=0

We calculate fractions


28x/14x^2+(-20x)/14x^2+2+6=0

We add all the numbers together, and all the variables

28x/14x^2+(-20x)/14x^2+8=0

We multiply all the terms by the denominator


28x+(-20x)+8*14x^2=0

Wy multiply elements

112x^2+28x+(-20x)=0

We get rid of parentheses

112x^2+28x-20x=0

We add all the numbers together, and all the variables

112x^2+8x=0

a = 112; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·112·0
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*112}=\frac{-16}{224}
=-1/14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*112}=\frac{0}{224}
=0
$