4=50x/x^2+25

Solution for 4=50x/x^2+25 equation:

4=50x/x^2+25

We move all terms to the left:

4-(50x/x^2+25)=0


Domain of the equation: x^2+25)!=0

x∈R


We get rid of parentheses

-50x/x^2-25+4=0

We multiply all the terms by the denominator


-50x-25*x^2+4*x^2=0

We add all the numbers together, and all the variables

-21x^2-50x=0

a = -21; b = -50; c = 0;
Δ = b2-4ac
Δ = -502-4·(-21)·0
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-50}{2*-21}=\frac{0}{-42}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+50}{2*-21}=\frac{100}{-42}
=-2+8/21
$