12+63x=12/x+63

Solution for 12+63x=12/x+63 equation:

12+63x=12/x+63

We move all terms to the left:

12+63x-(12/x+63)=0


Domain of the equation: x+63)!=0

x∈R


We get rid of parentheses

63x-12/x-63+12=0

We multiply all the terms by the denominator


63x*x-63*x+12*x-12=0

We add all the numbers together, and all the variables

-51x+63x*x-12=0

Wy multiply elements

63x^2-51x-12=0

a = 63; b = -51; c = -12;
Δ = b2-4ac
Δ = -512-4·63·(-12)
Δ = 5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5625}=75$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-75}{2*63}=\frac{-24}{126}
=-4/21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+75}{2*63}=\frac{126}{126}
=1
$