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

Solution for x^2=16(x+5+16) equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

x^2-(16(x+21))=0


We calculate terms in parentheses: -(16(x+21)), so:

16(x+21)

We multiply parentheses

16x+336

Back to the equation:

-(16x+336)


We get rid of parentheses

x^2-16x-336=0

a = 1; b = -16; c = -336;
Δ = b2-4ac
Δ = -162-4·1·(-336)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-40}{2*1}=\frac{-24}{2}
=-12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+40}{2*1}=\frac{56}{2}
=28
$