x-32=19-30/x

Solution for x-32=19-30/x equation:

x-32=19-30/x

We move all terms to the left:

x-32-(19-30/x)=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-(-30/x+19)-32=0

We get rid of parentheses

x+30/x-19-32=0

We multiply all the terms by the denominator


x*x-19*x-32*x+30=0

We add all the numbers together, and all the variables

-51x+x*x+30=0

Wy multiply elements

x^2-51x+30=0

a = 1; b = -51; c = +30;
Δ = b2-4ac
Δ = -512-4·1·30
Δ = 2481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-\sqrt{2481}}{2*1}=\frac{51-\sqrt{2481}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+\sqrt{2481}}{2*1}=\frac{51+\sqrt{2481}}{2}
$