.2x+51=(3000/x+5)

Solution for .2x+51=(3000/x+5) equation:

.2x+51=(3000/x+5)

We move all terms to the left:

.2x+51-((3000/x+5))=0


Domain of the equation: x+5))!=0

x∈R


We multiply all the terms by the denominator


(.2x)*x+51*x+5))-((3000+5))=0

We add all the numbers together, and all the variables

(+.2x)*x+51*x+5))-(3005)=0

We add all the numbers together, and all the variables

51x+(+.2x)*x=0

We multiply parentheses

x^2+51x=0

a = 1; b = 51; c = 0;
Δ = b2-4ac
Δ = 512-4·1·0
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-51}{2*1}=\frac{-102}{2}
=-51
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+51}{2*1}=\frac{0}{2}
=0
$