1/4x-2/7=1/2x=12

Solution for 1/4x-2/7=1/2x=12 equation:

1/4x-2/7=1/2x=12

We move all terms to the left:

1/4x-2/7-(1/2x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/4x-(+1/2x)-2/7=0

We get rid of parentheses

1/4x-1/2x-2/7=0

We calculate fractions


(-32x^2)/392x^2+98x/392x^2+(-196x)/392x^2=0

We multiply all the terms by the denominator


(-32x^2)+98x+(-196x)=0

We get rid of parentheses

-32x^2+98x-196x=0

We add all the numbers together, and all the variables

-32x^2-98x=0

a = -32; b = -98; c = 0;
Δ = b2-4ac
Δ = -982-4·(-32)·0
Δ = 9604
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9604}=98$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-98)-98}{2*-32}=\frac{0}{-64}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-98)+98}{2*-32}=\frac{196}{-64}
=-3+1/16
$