1/210x+6=8x-6

Solution for 1/210x+6=8x-6 equation:

1/210x+6=8x-6

We move all terms to the left:

1/210x+6-(8x-6)=0


Domain of the equation: 210x!=0

x!=0/210

x!=0

x∈R


We get rid of parentheses

1/210x-8x+6+6=0

We multiply all the terms by the denominator


-8x*210x+6*210x+6*210x+1=0

Wy multiply elements

-1680x^2+1260x+1260x+1=0

We add all the numbers together, and all the variables

-1680x^2+2520x+1=0

a = -1680; b = 2520; c = +1;
Δ = b2-4ac
Δ = 25202-4·(-1680)·1
Δ = 6357120
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:

$\sqrt{\Delta}=\sqrt{6357120}=\sqrt{64*99330}=\sqrt{64}*\sqrt{99330}=8\sqrt{99330}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2520)-8\sqrt{99330}}{2*-1680}=\frac{-2520-8\sqrt{99330}}{-3360}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2520)+8\sqrt{99330}}{2*-1680}=\frac{-2520+8\sqrt{99330}}{-3360}
$