x=42/(x-5)+4

Solution for x=42/(x-5)+4 equation:

x=42/(x-5)+4

We move all terms to the left:

x-(42/(x-5)+4)=0


Domain of the equation: (x-5)+4)!=0

x∈R


We multiply all the terms by the denominator


x*(x-5)+4)-(42=0

We add all the numbers together, and all the variables

x*(x-5)=0

We multiply parentheses

x^2-5x=0

a = 1; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·1·0
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{-(-5)-5}{2*1}=\frac{0}{2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*1}=\frac{10}{2}
=5
$