16x^2-6x=1

Solution for 16x^2-6x=1 equation:

16x^2-6x=1

We move all terms to the left:

16x^2-6x-(1)=0

a = 16; b = -6; c = -1;
Δ = b2-4ac
Δ = -62-4·16·(-1)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-10}{2*16}=\frac{-4}{32}
=-1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+10}{2*16}=\frac{16}{32}
=1/2
$