2/7x+12=6/4x-11

Solution for 2/7x+12=6/4x-11 equation:

2/7x+12=6/4x-11

We move all terms to the left:

2/7x+12-(6/4x-11)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 4x-11)!=0

x∈R


We get rid of parentheses

2/7x-6/4x+11+12=0

We calculate fractions


8x/28x^2+(-42x)/28x^2+11+12=0

We add all the numbers together, and all the variables

8x/28x^2+(-42x)/28x^2+23=0

We multiply all the terms by the denominator


8x+(-42x)+23*28x^2=0

Wy multiply elements

644x^2+8x+(-42x)=0

We get rid of parentheses

644x^2+8x-42x=0

We add all the numbers together, and all the variables

644x^2-34x=0

a = 644; b = -34; c = 0;
Δ = b2-4ac
Δ = -342-4·644·0
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-34}{2*644}=\frac{0}{1288}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+34}{2*644}=\frac{68}{1288}
=17/322
$