16x^2+1=40x

Solution for 16x^2+1=40x equation:

16x^2+1=40x

We move all terms to the left:

16x^2+1-(40x)=0

a = 16; b = -40; c = +1;
Δ = b2-4ac
Δ = -402-4·16·1
Δ = 1536
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:

$\sqrt{\Delta}=\sqrt{1536}=\sqrt{256*6}=\sqrt{256}*\sqrt{6}=16\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-16\sqrt{6}}{2*16}=\frac{40-16\sqrt{6}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+16\sqrt{6}}{2*16}=\frac{40+16\sqrt{6}}{32}
$