5/(7x2x)=7

Solution for 5/(7x2x)=7 equation:

5/(7x^2x)=7

We move all terms to the left:

5/(7x^2x)-(7)=0


Domain of the equation: 7x^2x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-7*7x^2x+5=0

Wy multiply elements

-49x^2+5=0

a = -49; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-49)·5
Δ = 980
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:

$\sqrt{\Delta}=\sqrt{980}=\sqrt{196*5}=\sqrt{196}*\sqrt{5}=14\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{5}}{2*-49}=\frac{0-14\sqrt{5}}{-98}
=-\frac{14\sqrt{5}}{-98}
=-\frac{\sqrt{5}}{-7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{5}}{2*-49}=\frac{0+14\sqrt{5}}{-98}
=\frac{14\sqrt{5}}{-98}
=\frac{\sqrt{5}}{-7}
$