(1/6)(6x+2)=5x

Solution for (1/6)(6x+2)=5x equation:

(1/6)(6x+2)=5x

We move all terms to the left:

(1/6)(6x+2)-(5x)=0


Domain of the equation: 6)(6x+2)!=0

x∈R


We add all the numbers together, and all the variables

(+1/6)(6x+2)-5x=0

We add all the numbers together, and all the variables

-5x+(+1/6)(6x+2)=0

We multiply parentheses ..

(+6x^2+1/6*2)-5x=0

We multiply all the terms by the denominator


(+6x^2+1-5x*6*2)=0

We get rid of parentheses

6x^2-5x*6*2+1=0

Wy multiply elements

6x^2-60x*2+1=0

Wy multiply elements

6x^2-120x+1=0

a = 6; b = -120; c = +1;
Δ = b2-4ac
Δ = -1202-4·6·1
Δ = 14376
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:

$\sqrt{\Delta}=\sqrt{14376}=\sqrt{4*3594}=\sqrt{4}*\sqrt{3594}=2\sqrt{3594}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-2\sqrt{3594}}{2*6}=\frac{120-2\sqrt{3594}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+2\sqrt{3594}}{2*6}=\frac{120+2\sqrt{3594}}{12}
$