x(6+5/7)=31

Solution for x(6+5/7)=31 equation:

x(6+5/7)=31

We move all terms to the left:

x(6+5/7)-(31)=0

We add all the numbers together, and all the variables

x(5/7+6)-31=0

We multiply parentheses

5x^2+6x-31=0

a = 5; b = 6; c = -31;
Δ = b2-4ac
Δ = 62-4·5·(-31)
Δ = 656
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:

$\sqrt{\Delta}=\sqrt{656}=\sqrt{16*41}=\sqrt{16}*\sqrt{41}=4\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4\sqrt{41}}{2*5}=\frac{-6-4\sqrt{41}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4\sqrt{41}}{2*5}=\frac{-6+4\sqrt{41}}{10}
$