X+4/(x-3)=20

Solution for X+4/(x-3)=20 equation:

X+4/(X-3)=20

We move all terms to the left:

X+4/(X-3)-(20)=0


Domain of the equation: (X-3)!=0

We move all terms containing X to the left, all other terms to the right

X!=3

X∈R


We multiply all the terms by the denominator


X*(X-3)-20*(X-3)+4=0

We multiply parentheses

X^2-3X-20X+60+4=0

We add all the numbers together, and all the variables

X^2-23X+64=0

a = 1; b = -23; c = +64;
Δ = b2-4ac
Δ = -232-4·1·64
Δ = 273
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{-(-23)-\sqrt{273}}{2*1}=\frac{23-\sqrt{273}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{273}}{2*1}=\frac{23+\sqrt{273}}{2}
$