x+7/6x=65

Solution for x+7/6x=65 equation:

x+7/6x=65

We move all terms to the left:

x+7/6x-(65)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We multiply all the terms by the denominator


x*6x-65*6x+7=0

Wy multiply elements

6x^2-390x+7=0

a = 6; b = -390; c = +7;
Δ = b2-4ac
Δ = -3902-4·6·7
Δ = 151932
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:

$\sqrt{\Delta}=\sqrt{151932}=\sqrt{4*37983}=\sqrt{4}*\sqrt{37983}=2\sqrt{37983}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-390)-2\sqrt{37983}}{2*6}=\frac{390-2\sqrt{37983}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-390)+2\sqrt{37983}}{2*6}=\frac{390+2\sqrt{37983}}{12}
$