1600+x^2=16x^2+40x+25

Solution for 1600+x^2=16x^2+40x+25 equation:

1600+x^2=16x^2+40x+25

We move all terms to the left:

1600+x^2-(16x^2+40x+25)=0

We get rid of parentheses

x^2-16x^2-40x-25+1600=0

We add all the numbers together, and all the variables

-15x^2-40x+1575=0

a = -15; b = -40; c = +1575;
Δ = b2-4ac
Δ = -402-4·(-15)·1575
Δ = 96100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{96100}=310$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-310}{2*-15}=\frac{-270}{-30}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+310}{2*-15}=\frac{350}{-30}
=-11+2/3
$