x(x+2)=5/7-x

Solution for x(x+2)=5/7-x equation:

x(x+2)=5/7-x

We move all terms to the left:

x(x+2)-(5/7-x)=0


Domain of the equation: 7-x)!=0

We move all terms containing x to the left, all other terms to the right

-x)!=-7

x!=-7/1

x!=-7

x∈R


We add all the numbers together, and all the variables

x(x+2)-(-1x+5/7)=0

We multiply parentheses

x^2+2x-(-1x+5/7)=0

We get rid of parentheses

x^2+2x+1x-5/7=0

We multiply all the terms by the denominator


x^2*7+2x*7+1x*7-5=0

Wy multiply elements

7x^2+14x+7x-5=0

We add all the numbers together, and all the variables

7x^2+21x-5=0

a = 7; b = 21; c = -5;
Δ = b2-4ac
Δ = 212-4·7·(-5)
Δ = 581
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-\sqrt{581}}{2*7}=\frac{-21-\sqrt{581}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{581}}{2*7}=\frac{-21+\sqrt{581}}{14}
$