24+x=4/x+1

Solution for 24+x=4/x+1 equation:

24+x=4/x+1

We move all terms to the left:

24+x-(4/x+1)=0


Domain of the equation: x+1)!=0

x∈R


We get rid of parentheses

x-4/x-1+24=0

We multiply all the terms by the denominator


x*x-1*x+24*x-4=0

We add all the numbers together, and all the variables

23x+x*x-4=0

Wy multiply elements

x^2+23x-4=0

a = 1; b = 23; c = -4;
Δ = b2-4ac
Δ = 232-4·1·(-4)
Δ = 545
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{545}}{2*1}=\frac{-23-\sqrt{545}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+\sqrt{545}}{2*1}=\frac{-23+\sqrt{545}}{2}
$