0.08x+52-(1310/x)=0

Solution for 0.08x+52-(1310/x)=0 equation:

0.08x+52-(1310/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

0.08x-(+1310/x)+52=0

We get rid of parentheses

0.08x-1310/x+52=0

We multiply all the terms by the denominator


(0.08x)*x+52*x-1310=0

We add all the numbers together, and all the variables

(+0.08x)*x+52*x-1310=0

We add all the numbers together, and all the variables

52x+(+0.08x)*x-1310=0

We multiply parentheses

0x^2+52x-1310=0

We add all the numbers together, and all the variables

x^2+52x-1310=0

a = 1; b = 52; c = -1310;
Δ = b2-4ac
Δ = 522-4·1·(-1310)
Δ = 7944
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:

$\sqrt{\Delta}=\sqrt{7944}=\sqrt{4*1986}=\sqrt{4}*\sqrt{1986}=2\sqrt{1986}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-2\sqrt{1986}}{2*1}=\frac{-52-2\sqrt{1986}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+2\sqrt{1986}}{2*1}=\frac{-52+2\sqrt{1986}}{2}
$