7x+1/5x=72

Solution for 7x+1/5x=72 equation:

7x+1/5x=72

We move all terms to the left:

7x+1/5x-(72)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


7x*5x-72*5x+1=0

Wy multiply elements

35x^2-360x+1=0

a = 35; b = -360; c = +1;
Δ = b2-4ac
Δ = -3602-4·35·1
Δ = 129460
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:

$\sqrt{\Delta}=\sqrt{129460}=\sqrt{4*32365}=\sqrt{4}*\sqrt{32365}=2\sqrt{32365}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-2\sqrt{32365}}{2*35}=\frac{360-2\sqrt{32365}}{70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+2\sqrt{32365}}{2*35}=\frac{360+2\sqrt{32365}}{70}
$