x(x+2)+(x-1)2x-1=17

Solution for x(x+2)+(x-1)2x-1=17 equation:

x(x+2)+(x-1)2x-1=17

We move all terms to the left:

x(x+2)+(x-1)2x-1-(17)=0

We add all the numbers together, and all the variables

x(x+2)+(x-1)2x-18=0

We multiply parentheses

x^2+2x^2+2x-2x-18=0

We add all the numbers together, and all the variables

3x^2-18=0

a = 3; b = 0; c = -18;
Δ = b2-4ac
Δ = 02-4·3·(-18)
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{6}}{2*3}=\frac{0-6\sqrt{6}}{6}
=-\frac{6\sqrt{6}}{6}
=-\sqrt{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{6}}{2*3}=\frac{0+6\sqrt{6}}{6}
=\frac{6\sqrt{6}}{6}
=\sqrt{6}
$