7/x+1+1/6x+6=4

Solution for 7/x+1+1/6x+6=4 equation:

7/x+1+1/6x+6=4

We move all terms to the left:

7/x+1+1/6x+6-(4)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

7/x+1/6x+3=0

We calculate fractions


42x/6x^2+x/6x^2+3=0

We multiply all the terms by the denominator


42x+x+3*6x^2=0

We add all the numbers together, and all the variables

43x+3*6x^2=0

Wy multiply elements

18x^2+43x=0

a = 18; b = 43; c = 0;
Δ = b2-4ac
Δ = 432-4·18·0
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(43)-43}{2*18}=\frac{-86}{36}
=-2+7/18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+43}{2*18}=\frac{0}{36}
=0
$