(x-1)x+(x.2)3=126

Solution for (x-1)x+(x.2)3=126 equation:

(x-1)x+(x.2)3=126

We move all terms to the left:

(x-1)x+(x.2)3-(126)=0

We add all the numbers together, and all the variables

(x-1)x+(+x.2)3-126=0

We multiply parentheses

x^2-1x+3x-126=0

We add all the numbers together, and all the variables

x^2+2x-126=0

a = 1; b = 2; c = -126;
Δ = b2-4ac
Δ = 22-4·1·(-126)
Δ = 508
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:

$\sqrt{\Delta}=\sqrt{508}=\sqrt{4*127}=\sqrt{4}*\sqrt{127}=2\sqrt{127}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{127}}{2*1}=\frac{-2-2\sqrt{127}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{127}}{2*1}=\frac{-2+2\sqrt{127}}{2}
$