6/x=-x+7

Solution for 6/x=-x+7 equation:

6/x=-x+7

We move all terms to the left:

6/x-(-x+7)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

6/x+1x-7=0

We multiply all the terms by the denominator


1x*x-7*x+6=0

We add all the numbers together, and all the variables

-7x+1x*x+6=0

Wy multiply elements

x^2-7x+6=0

a = 1; b = -7; c = +6;
Δ = b2-4ac
Δ = -72-4·1·6
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-5}{2*1}=\frac{2}{2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+5}{2*1}=\frac{12}{2}
=6
$