1/28x-12+2=6x-6

Solution for 1/28x-12+2=6x-6 equation:

1/28x-12+2=6x-6

We move all terms to the left:

1/28x-12+2-(6x-6)=0


Domain of the equation: 28x!=0

x!=0/28

x!=0

x∈R


We add all the numbers together, and all the variables

1/28x-(6x-6)-10=0

We get rid of parentheses

1/28x-6x+6-10=0

We multiply all the terms by the denominator


-6x*28x+6*28x-10*28x+1=0

Wy multiply elements

-168x^2+168x-280x+1=0

We add all the numbers together, and all the variables

-168x^2-112x+1=0

a = -168; b = -112; c = +1;
Δ = b2-4ac
Δ = -1122-4·(-168)·1
Δ = 13216
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:

$\sqrt{\Delta}=\sqrt{13216}=\sqrt{16*826}=\sqrt{16}*\sqrt{826}=4\sqrt{826}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-112)-4\sqrt{826}}{2*-168}=\frac{112-4\sqrt{826}}{-336}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+4\sqrt{826}}{2*-168}=\frac{112+4\sqrt{826}}{-336}
$