2x+18=16x^2-144

Solution for 2x+18=16x^2-144 equation:

2x+18=16x^2-144

We move all terms to the left:

2x+18-(16x^2-144)=0

We get rid of parentheses

-16x^2+2x+144+18=0

We add all the numbers together, and all the variables

-16x^2+2x+162=0

a = -16; b = 2; c = +162;
Δ = b2-4ac
Δ = 22-4·(-16)·162
Δ = 10372
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:

$\sqrt{\Delta}=\sqrt{10372}=\sqrt{4*2593}=\sqrt{4}*\sqrt{2593}=2\sqrt{2593}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{2593}}{2*-16}=\frac{-2-2\sqrt{2593}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{2593}}{2*-16}=\frac{-2+2\sqrt{2593}}{-32}
$