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+294x+2=0

a = -21; b = 294; c = +2;
Δ = b2-4ac
Δ = 2942-4·(-21)·2
Δ = 86604
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:

$\sqrt{\Delta}=\sqrt{86604}=\sqrt{4*21651}=\sqrt{4}*\sqrt{21651}=2\sqrt{21651}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(294)-2\sqrt{21651}}{2*-21}=\frac{-294-2\sqrt{21651}}{-42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(294)+2\sqrt{21651}}{2*-21}=\frac{-294+2\sqrt{21651}}{-42}
$