12/x+63=74-2x

Solution for 12/x+63=74-2x equation:

12/x+63=74-2x

We move all terms to the left:

12/x+63-(74-2x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

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
$