x+(x+14)=(x+2)7x

Solution for x+(x+14)=(x+2)7x equation:

x+(x+14)=(x+2)7x

We move all terms to the left:

x+(x+14)-((x+2)7x)=0

We get rid of parentheses

x+x-((x+2)7x)+14=0


We calculate terms in parentheses: -((x+2)7x), so:

(x+2)7x

We multiply parentheses

7x^2+14x

Back to the equation:

-(7x^2+14x)


We add all the numbers together, and all the variables

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

We get rid of parentheses

-7x^2+2x-14x+14=0

We add all the numbers together, and all the variables

-7x^2-12x+14=0

a = -7; b = -12; c = +14;
Δ = b2-4ac
Δ = -122-4·(-7)·14
Δ = 536
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:

$\sqrt{\Delta}=\sqrt{536}=\sqrt{4*134}=\sqrt{4}*\sqrt{134}=2\sqrt{134}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{134}}{2*-7}=\frac{12-2\sqrt{134}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{134}}{2*-7}=\frac{12+2\sqrt{134}}{-14}
$