1/X+2y=7

Solution for 1/X+2y=7 equation:

1/X+2X=7

We move all terms to the left:

1/X+2X-(7)=0


Domain of the equation: X!=0

X∈R


We add all the numbers together, and all the variables

2X+1/X-7=0

We multiply all the terms by the denominator


2X*X-7*X+1=0

We add all the numbers together, and all the variables

-7X+2X*X+1=0

Wy multiply elements

2X^2-7X+1=0

a = 2; b = -7; c = +1;
Δ = b2-4ac
Δ = -72-4·2·1
Δ = 41
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{41}}{2*2}=\frac{7-\sqrt{41}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{41}}{2*2}=\frac{7+\sqrt{41}}{4}
$