x+2/7x=27

Solution for x+2/7x=27 equation:

x+2/7x=27

We move all terms to the left:

x+2/7x-(27)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We multiply all the terms by the denominator


x*7x-27*7x+2=0

Wy multiply elements

7x^2-189x+2=0

a = 7; b = -189; c = +2;
Δ = b2-4ac
Δ = -1892-4·7·2
Δ = 35665
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{-(-189)-\sqrt{35665}}{2*7}=\frac{189-\sqrt{35665}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-189)+\sqrt{35665}}{2*7}=\frac{189+\sqrt{35665}}{14}
$