x=(1/7)(7x+14)

Solution for x=(1/7)(7x+14) equation:

x=(1/7)(7x+14)

We move all terms to the left:

x-((1/7)(7x+14))=0


Domain of the equation: 7)(7x+14))!=0

x∈R


We add all the numbers together, and all the variables

x-((+1/7)(7x+14))=0

We multiply parentheses ..

-((+7x^2+1/7*14))+x=0

We multiply all the terms by the denominator


-((+7x^2+1+x*7*14))=0


We calculate terms in parentheses: -((+7x^2+1+x*7*14)), so:

(+7x^2+1+x*7*14)

We get rid of parentheses

7x^2+x*7*14+1

Wy multiply elements

7x^2+98x*1+1

Wy multiply elements

7x^2+98x+1

Back to the equation:

-(7x^2+98x+1)


We get rid of parentheses

-7x^2-98x-1=0

a = -7; b = -98; c = -1;
Δ = b2-4ac
Δ = -982-4·(-7)·(-1)
Δ = 9576
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:

$\sqrt{\Delta}=\sqrt{9576}=\sqrt{36*266}=\sqrt{36}*\sqrt{266}=6\sqrt{266}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-98)-6\sqrt{266}}{2*-7}=\frac{98-6\sqrt{266}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-98)+6\sqrt{266}}{2*-7}=\frac{98+6\sqrt{266}}{-14}
$