1+x-3/x+7=40/x+7

Solution for 1+x-3/x+7=40/x+7 equation:

1+x-3/x+7=40/x+7

We move all terms to the left:

1+x-3/x+7-(40/x+7)=0


Domain of the equation: x!=0

x∈R



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

x∈R


We add all the numbers together, and all the variables

x-3/x-(40/x+7)+8=0

We get rid of parentheses

x-3/x-40/x-7+8=0

We multiply all the terms by the denominator


x*x-7*x+8*x-3-40=0

We add all the numbers together, and all the variables

x+x*x-43=0

Wy multiply elements

x^2+x-43=0

a = 1; b = 1; c = -43;
Δ = b2-4ac
Δ = 12-4·1·(-43)
Δ = 173
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{-(1)-\sqrt{173}}{2*1}=\frac{-1-\sqrt{173}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{173}}{2*1}=\frac{-1+\sqrt{173}}{2}
$