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12+63x=12/x+63
We move all terms to the left:
12+63x-(12/x+63)=0
Domain of the equation: x+63)!=0We get rid of parentheses
x∈R
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 $
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