X=2(42)/x+5

Solution for X=2(42)/x+5 equation:

X=2(42)/X+5

We move all terms to the left:

X-(2(42)/X+5)=0


Domain of the equation: X+5)!=0

X∈R


We get rid of parentheses

X-242/X-5=0

We multiply all the terms by the denominator


X*X-5*X-242=0

We add all the numbers together, and all the variables

-5X+X*X-242=0

Wy multiply elements

X^2-5X-242=0

a = 1; b = -5; c = -242;
Δ = b2-4ac
Δ = -52-4·1·(-242)
Δ = 993
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{-(-5)-\sqrt{993}}{2*1}=\frac{5-\sqrt{993}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{993}}{2*1}=\frac{5+\sqrt{993}}{2}
$