x(x+16)+(x*2)=267

Solution for x(x+16)+(x*2)=267 equation:

x(x+16)+(x*2)=267

We move all terms to the left:

x(x+16)+(x*2)-(267)=0

We add all the numbers together, and all the variables

x(x+16)+(+x*2)-267=0

We multiply parentheses

x^2+16x+(+x*2)-267=0

We get rid of parentheses

x^2+16x+x*2-267=0

Wy multiply elements

x^2+16x+2x-267=0

We add all the numbers together, and all the variables

x^2+18x-267=0

a = 1; b = 18; c = -267;
Δ = b2-4ac
Δ = 182-4·1·(-267)
Δ = 1392
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:

$\sqrt{\Delta}=\sqrt{1392}=\sqrt{16*87}=\sqrt{16}*\sqrt{87}=4\sqrt{87}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-4\sqrt{87}}{2*1}=\frac{-18-4\sqrt{87}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+4\sqrt{87}}{2*1}=\frac{-18+4\sqrt{87}}{2}
$