(1800+25,5x)/x=50x

Solution for (1800+25,5x)/x=50x equation:

(1800+25.5x)/x=50x

We move all terms to the left:

(1800+25.5x)/x-(50x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

(25.5x+1800)/x-50x=0

We add all the numbers together, and all the variables

-50x+(25.5x+1800)/x=0

We multiply all the terms by the denominator


-50x*x+(25.5x+1800)=0

Wy multiply elements

-50x^2+(25.5x+1800)=0

We get rid of parentheses

-50x^2+25.5x+1800=0

a = -50; b = 25.5; c = +1800;
Δ = b2-4ac
Δ = 25.52-4·(-50)·1800
Δ = 360650.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25.5)-\sqrt{360650.25}}{2*-50}=\frac{-25.5-\sqrt{360650.25}}{-100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25.5)+\sqrt{360650.25}}{2*-50}=\frac{-25.5+\sqrt{360650.25}}{-100}
$