5/2x+550=25x

Solution for 5/2x+550=25x equation:

5/2x+550=25x

We move all terms to the left:

5/2x+550-(25x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-25x+5/2x+550=0

We multiply all the terms by the denominator


-25x*2x+550*2x+5=0

Wy multiply elements

-50x^2+1100x+5=0

a = -50; b = 1100; c = +5;
Δ = b2-4ac
Δ = 11002-4·(-50)·5
Δ = 1211000
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:

$\sqrt{\Delta}=\sqrt{1211000}=\sqrt{100*12110}=\sqrt{100}*\sqrt{12110}=10\sqrt{12110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1100)-10\sqrt{12110}}{2*-50}=\frac{-1100-10\sqrt{12110}}{-100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1100)+10\sqrt{12110}}{2*-50}=\frac{-1100+10\sqrt{12110}}{-100}
$