0.2x+51=(3000)/x+5

Solution for 0.2x+51=(3000)/x+5 equation:

0.2x+51=(3000)/x+5

We move all terms to the left:

0.2x+51-((3000)/x+5)=0


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

x∈R


We get rid of parentheses

0.2x-3000/x-5+51=0

We multiply all the terms by the denominator


(0.2x)*x-5*x+51*x-3000=0

We add all the numbers together, and all the variables

(+0.2x)*x-5*x+51*x-3000=0

We add all the numbers together, and all the variables

46x+(+0.2x)*x-3000=0

We multiply parentheses

0x^2+46x-3000=0

We add all the numbers together, and all the variables

x^2+46x-3000=0

a = 1; b = 46; c = -3000;
Δ = b2-4ac
Δ = 462-4·1·(-3000)
Δ = 14116
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:

$\sqrt{\Delta}=\sqrt{14116}=\sqrt{4*3529}=\sqrt{4}*\sqrt{3529}=2\sqrt{3529}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-2\sqrt{3529}}{2*1}=\frac{-46-2\sqrt{3529}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+2\sqrt{3529}}{2*1}=\frac{-46+2\sqrt{3529}}{2}
$