x+2/7x=36

Solution for x+2/7x=36 equation:

x+2/7x=36

We move all terms to the left:

x+2/7x-(36)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We multiply all the terms by the denominator


x*7x-36*7x+2=0

Wy multiply elements

7x^2-252x+2=0

a = 7; b = -252; c = +2;
Δ = b2-4ac
Δ = -2522-4·7·2
Δ = 63448
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:

$\sqrt{\Delta}=\sqrt{63448}=\sqrt{4*15862}=\sqrt{4}*\sqrt{15862}=2\sqrt{15862}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-252)-2\sqrt{15862}}{2*7}=\frac{252-2\sqrt{15862}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-252)+2\sqrt{15862}}{2*7}=\frac{252+2\sqrt{15862}}{14}
$