2/21x+8=x+6

Solution for 2/21x+8=x+6 equation:

2/21x+8=x+6

We move all terms to the left:

2/21x+8-(x+6)=0


Domain of the equation: 21x!=0

x!=0/21

x!=0

x∈R


We get rid of parentheses

2/21x-x-6+8=0

We multiply all the terms by the denominator


-x*21x-6*21x+8*21x+2=0

Wy multiply elements

-21x^2-126x+168x+2=0

We add all the numbers together, and all the variables

-21x^2+42x+2=0

a = -21; b = 42; c = +2;
Δ = b2-4ac
Δ = 422-4·(-21)·2
Δ = 1932
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:

$\sqrt{\Delta}=\sqrt{1932}=\sqrt{4*483}=\sqrt{4}*\sqrt{483}=2\sqrt{483}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{483}}{2*-21}=\frac{-42-2\sqrt{483}}{-42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{483}}{2*-21}=\frac{-42+2\sqrt{483}}{-42}
$