(21+x)*(21/x)=147

Solution for (21+x)*(21/x)=147 equation:

(21+x)(21/x)=147

We move all terms to the left:

(21+x)(21/x)-(147)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(x+21)(+21/x)-147=0

We multiply parentheses ..

(+21x^2+441x)-147=0

We get rid of parentheses

21x^2+441x-147=0

a = 21; b = 441; c = -147;
Δ = b2-4ac
Δ = 4412-4·21·(-147)
Δ = 206829
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{206829}=\sqrt{441*469}=\sqrt{441}*\sqrt{469}=21\sqrt{469}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(441)-21\sqrt{469}}{2*21}=\frac{-441-21\sqrt{469}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(441)+21\sqrt{469}}{2*21}=\frac{-441+21\sqrt{469}}{42}
$