6x(2x-9)=-31

Solution for 6x(2x-9)=-31 equation:

6x(2x-9)=-31

We move all terms to the left:

6x(2x-9)-(-31)=0

We add all the numbers together, and all the variables

6x(2x-9)+31=0

We multiply parentheses

12x^2-54x+31=0

a = 12; b = -54; c = +31;
Δ = b2-4ac
Δ = -542-4·12·31
Δ = 1428
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:

$\sqrt{\Delta}=\sqrt{1428}=\sqrt{4*357}=\sqrt{4}*\sqrt{357}=2\sqrt{357}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-2\sqrt{357}}{2*12}=\frac{54-2\sqrt{357}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+2\sqrt{357}}{2*12}=\frac{54+2\sqrt{357}}{24}
$