x=-5/x+7

Solution for x=-5/x+7 equation:

x=-5/x+7

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

x+5/x-7=0

We multiply all the terms by the denominator


x*x-7*x+5=0

We add all the numbers together, and all the variables

-7x+x*x+5=0

Wy multiply elements

x^2-7x+5=0

a = 1; b = -7; c = +5;
Δ = b2-4ac
Δ = -72-4·1·5
Δ = 29
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{-(-7)-\sqrt{29}}{2*1}=\frac{7-\sqrt{29}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{29}}{2*1}=\frac{7+\sqrt{29}}{2}
$