x+x2+3x-6=31

Solution for x+x2+3x-6=31 equation:

x+x2+3x-6=31

We move all terms to the left:

x+x2+3x-6-(31)=0

We add all the numbers together, and all the variables

x^2+4x-37=0

a = 1; b = 4; c = -37;
Δ = b2-4ac
Δ = 42-4·1·(-37)
Δ = 164
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:

$\sqrt{\Delta}=\sqrt{164}=\sqrt{4*41}=\sqrt{4}*\sqrt{41}=2\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{41}}{2*1}=\frac{-4-2\sqrt{41}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{41}}{2*1}=\frac{-4+2\sqrt{41}}{2}
$