6/7x+7=2/4x+12

Solution for 6/7x+7=2/4x+12 equation:

6/7x+7=2/4x+12

We move all terms to the left:

6/7x+7-(2/4x+12)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 4x+12)!=0

x∈R


We get rid of parentheses

6/7x-2/4x-12+7=0

We calculate fractions


24x/28x^2+(-14x)/28x^2-12+7=0

We add all the numbers together, and all the variables

24x/28x^2+(-14x)/28x^2-5=0

We multiply all the terms by the denominator


24x+(-14x)-5*28x^2=0

Wy multiply elements

-140x^2+24x+(-14x)=0

We get rid of parentheses

-140x^2+24x-14x=0

We add all the numbers together, and all the variables

-140x^2+10x=0

a = -140; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-140)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-140}=\frac{-20}{-280}
=1/14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-140}=\frac{0}{-280}
=0
$