X+8=1/7x-2

Solution for X+8=1/7x-2 equation:

X+8=1/7X-2

We move all terms to the left:

X+8-(1/7X-2)=0


Domain of the equation: 7X-2)!=0

X∈R


We get rid of parentheses

X-1/7X+2+8=0

We multiply all the terms by the denominator


X*7X+2*7X+8*7X-1=0

Wy multiply elements

7X^2+14X+56X-1=0

We add all the numbers together, and all the variables

7X^2+70X-1=0

a = 7; b = 70; c = -1;
Δ = b2-4ac
Δ = 702-4·7·(-1)
Δ = 4928
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:

$\sqrt{\Delta}=\sqrt{4928}=\sqrt{64*77}=\sqrt{64}*\sqrt{77}=8\sqrt{77}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-8\sqrt{77}}{2*7}=\frac{-70-8\sqrt{77}}{14}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+8\sqrt{77}}{2*7}=\frac{-70+8\sqrt{77}}{14}
$