6/11x+7x=6

Solution for 6/11x+7x=6 equation:

6/11x+7x=6

We move all terms to the left:

6/11x+7x-(6)=0


Domain of the equation: 11x!=0

x!=0/11

x!=0

x∈R


We add all the numbers together, and all the variables

7x+6/11x-6=0

We multiply all the terms by the denominator


7x*11x-6*11x+6=0

Wy multiply elements

77x^2-66x+6=0

a = 77; b = -66; c = +6;
Δ = b2-4ac
Δ = -662-4·77·6
Δ = 2508
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:

$\sqrt{\Delta}=\sqrt{2508}=\sqrt{4*627}=\sqrt{4}*\sqrt{627}=2\sqrt{627}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-2\sqrt{627}}{2*77}=\frac{66-2\sqrt{627}}{154}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+2\sqrt{627}}{2*77}=\frac{66+2\sqrt{627}}{154}
$