14x+28/49x-49=0

Solution for 14x+28/49x-49=0 equation:

14x+28/49x-49=0


Domain of the equation: 49x!=0

x!=0/49

x!=0

x∈R


We multiply all the terms by the denominator


14x*49x-49*49x+28=0

Wy multiply elements

686x^2-2401x+28=0

a = 686; b = -2401; c = +28;
Δ = b2-4ac
Δ = -24012-4·686·28
Δ = 5687969
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:

$\sqrt{\Delta}=\sqrt{5687969}=\sqrt{2401*2369}=\sqrt{2401}*\sqrt{2369}=49\sqrt{2369}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2401)-49\sqrt{2369}}{2*686}=\frac{2401-49\sqrt{2369}}{1372}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2401)+49\sqrt{2369}}{2*686}=\frac{2401+49\sqrt{2369}}{1372}
$