2/49x^-2+14x=0

Solution for 2/49x^-2+14x=0 equation:

2/49x^-2+14x=0


Domain of the equation: 49x^!=0

x!=0/49

x!=0

x∈R


We add all the numbers together, and all the variables

14x+2/49x^-2=0

We multiply all the terms by the denominator


14x*49x^-2*49x^+2=0

Wy multiply elements

686x^2-98x+2=0

a = 686; b = -98; c = +2;
Δ = b2-4ac
Δ = -982-4·686·2
Δ = 4116
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:

$\sqrt{\Delta}=\sqrt{4116}=\sqrt{196*21}=\sqrt{196}*\sqrt{21}=14\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-98)-14\sqrt{21}}{2*686}=\frac{98-14\sqrt{21}}{1372}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-98)+14\sqrt{21}}{2*686}=\frac{98+14\sqrt{21}}{1372}
$