18+0.50x=12+0.75x/x=24

Solution for 18+0.50x=12+0.75x/x=24 equation:

18+0.50x=12+0.75x/x=24

We move all terms to the left:

18+0.50x-(12+0.75x/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

0.50x-(0.75x/x+12)+18=0

We get rid of parentheses

0.50x-0.75x/x-12+18=0

We multiply all the terms by the denominator


(0.50x)*x-0.75x-12*x+18*x=0

We add all the numbers together, and all the variables

(+0.50x)*x-0.75x-12*x+18*x=0

We add all the numbers together, and all the variables

5.25x+(+0.50x)*x=0

We multiply parentheses

0x^2+5.25x=0

We add all the numbers together, and all the variables

x^2+5.25x=0

a = 1; b = 5.25; c = 0;
Δ = b2-4ac
Δ = 5.252-4·1·0
Δ = 27.5625
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{-(5.25)-\sqrt{27.5625}}{2*1}=\frac{-5.25-\sqrt{27.5625}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5.25)+\sqrt{27.5625}}{2*1}=\frac{-5.25+\sqrt{27.5625}}{2}
$