x+7/5x=26

Solution for x+7/5x=26 equation:

x+7/5x=26

We move all terms to the left:

x+7/5x-(26)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


x*5x-26*5x+7=0

Wy multiply elements

5x^2-130x+7=0

a = 5; b = -130; c = +7;
Δ = b2-4ac
Δ = -1302-4·5·7
Δ = 16760
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:

$\sqrt{\Delta}=\sqrt{16760}=\sqrt{4*4190}=\sqrt{4}*\sqrt{4190}=2\sqrt{4190}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-2\sqrt{4190}}{2*5}=\frac{130-2\sqrt{4190}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+2\sqrt{4190}}{2*5}=\frac{130+2\sqrt{4190}}{10}
$