40-25x=83/50x-1000

Solution for 40-25x=83/50x-1000 equation:

40-25x=83/50x-1000

We move all terms to the left:

40-25x-(83/50x-1000)=0


Domain of the equation: 50x-1000)!=0

x∈R


We get rid of parentheses

-25x-83/50x+1000+40=0

We multiply all the terms by the denominator


-25x*50x+1000*50x+40*50x-83=0

Wy multiply elements

-1250x^2+50000x+2000x-83=0

We add all the numbers together, and all the variables

-1250x^2+52000x-83=0

a = -1250; b = 52000; c = -83;
Δ = b2-4ac
Δ = 520002-4·(-1250)·(-83)
Δ = 2703585000
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:

$\sqrt{\Delta}=\sqrt{2703585000}=\sqrt{2500*1081434}=\sqrt{2500}*\sqrt{1081434}=50\sqrt{1081434}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52000)-50\sqrt{1081434}}{2*-1250}=\frac{-52000-50\sqrt{1081434}}{-2500}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52000)+50\sqrt{1081434}}{2*-1250}=\frac{-52000+50\sqrt{1081434}}{-2500}
$