5x+1/7x=21

Solution for 5x+1/7x=21 equation:

5x+1/7x=21

We move all terms to the left:

5x+1/7x-(21)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We multiply all the terms by the denominator


5x*7x-21*7x+1=0

Wy multiply elements

35x^2-147x+1=0

a = 35; b = -147; c = +1;
Δ = b2-4ac
Δ = -1472-4·35·1
Δ = 21469
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-147)-\sqrt{21469}}{2*35}=\frac{147-\sqrt{21469}}{70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-147)+\sqrt{21469}}{2*35}=\frac{147+\sqrt{21469}}{70}
$