2/7x+6=x+12

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

2/7x+6=x+12

We move all terms to the left:

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


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


-x*7x-12*7x+6*7x+2=0

Wy multiply elements

-7x^2-84x+42x+2=0

We add all the numbers together, and all the variables

-7x^2-42x+2=0

a = -7; b = -42; c = +2;
Δ = b2-4ac
Δ = -422-4·(-7)·2
Δ = 1820
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1820}=\sqrt{4*455}=\sqrt{4}*\sqrt{455}=2\sqrt{455}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{455}}{2*-7}=\frac{42-2\sqrt{455}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{455}}{2*-7}=\frac{42+2\sqrt{455}}{-14}
$