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12/x+63=74-2x
We move all terms to the left:
12/x+63-(74-2x)=0
Domain of the equation: x!=0We add all the numbers together, and all the variables
x∈R
12/x-(-2x+74)+63=0
We get rid of parentheses
12/x+2x-74+63=0
We multiply all the terms by the denominator
2x*x-74*x+63*x+12=0
We add all the numbers together, and all the variables
-11x+2x*x+12=0
Wy multiply elements
2x^2-11x+12=0
a = 2; b = -11; c = +12;
Δ = b2-4ac
Δ = -112-4·2·12
Δ = 25
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{25}=5$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-5}{2*2}=\frac{6}{4} =1+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+5}{2*2}=\frac{16}{4} =4 $
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