9+6x+x^2=160

Solution for 9+6x+x^2=160 equation:

9+6x+x^2=160

We move all terms to the left:

9+6x+x^2-(160)=0

We add all the numbers together, and all the variables

x^2+6x-151=0

a = 1; b = 6; c = -151;
Δ = b2-4ac
Δ = 62-4·1·(-151)
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-8\sqrt{10}}{2*1}=\frac{-6-8\sqrt{10}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+8\sqrt{10}}{2*1}=\frac{-6+8\sqrt{10}}{2}
$