7x+7/5x=7

Solution for 7x+7/5x=7 equation:

7x+7/5x=7

We move all terms to the left:

7x+7/5x-(7)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

35x^2-35x+7=0

a = 35; b = -35; c = +7;
Δ = b2-4ac
Δ = -352-4·35·7
Δ = 245
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:

$\sqrt{\Delta}=\sqrt{245}=\sqrt{49*5}=\sqrt{49}*\sqrt{5}=7\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-7\sqrt{5}}{2*35}=\frac{35-7\sqrt{5}}{70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+7\sqrt{5}}{2*35}=\frac{35+7\sqrt{5}}{70}
$