24+4.50x=200/x-1

Solution for 24+4.50x=200/x-1 equation:

24+4.50x=200/x-1

We move all terms to the left:

24+4.50x-(200/x-1)=0


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

x∈R


We get rid of parentheses

4.50x-200/x+1+24=0

We multiply all the terms by the denominator


(4.50x)*x+1*x+24*x-200=0

We add all the numbers together, and all the variables

(+4.50x)*x+1*x+24*x-200=0

We add all the numbers together, and all the variables

25x+(+4.50x)*x-200=0

We multiply parentheses

4x^2+25x-200=0

a = 4; b = 25; c = -200;
Δ = b2-4ac
Δ = 252-4·4·(-200)
Δ = 3825
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3825}=\sqrt{225*17}=\sqrt{225}*\sqrt{17}=15\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-15\sqrt{17}}{2*4}=\frac{-25-15\sqrt{17}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+15\sqrt{17}}{2*4}=\frac{-25+15\sqrt{17}}{8}
$