100x+3=-1/78x

Solution for 100x+3=-1/78x equation:

100x+3=-1/78x

We move all terms to the left:

100x+3-(-1/78x)=0


Domain of the equation: 78x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

100x+1/78x+3=0

We multiply all the terms by the denominator


100x*78x+3*78x+1=0

Wy multiply elements

7800x^2+234x+1=0

a = 7800; b = 234; c = +1;
Δ = b2-4ac
Δ = 2342-4·7800·1
Δ = 23556
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:

$\sqrt{\Delta}=\sqrt{23556}=\sqrt{4*5889}=\sqrt{4}*\sqrt{5889}=2\sqrt{5889}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(234)-2\sqrt{5889}}{2*7800}=\frac{-234-2\sqrt{5889}}{15600}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(234)+2\sqrt{5889}}{2*7800}=\frac{-234+2\sqrt{5889}}{15600}
$