x+5=2x^2-16

Solution for x+5=2x^2-16 equation:

x+5=2x^2-16

We move all terms to the left:

x+5-(2x^2-16)=0

We get rid of parentheses

-2x^2+x+16+5=0

We add all the numbers together, and all the variables

-2x^2+x+21=0

a = -2; b = 1; c = +21;
Δ = b2-4ac
Δ = 12-4·(-2)·21
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-13}{2*-2}=\frac{-14}{-4}
=3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+13}{2*-2}=\frac{12}{-4}
=-3
$