16x^2-24x=1

Solution for 16x^2-24x=1 equation:

16x^2-24x=1

We move all terms to the left:

16x^2-24x-(1)=0

a = 16; b = -24; c = -1;
Δ = b2-4ac
Δ = -242-4·16·(-1)
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{10}}{2*16}=\frac{24-8\sqrt{10}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{10}}{2*16}=\frac{24+8\sqrt{10}}{32}
$