46q^2-45q-1=0

Solution for 46q^2-45q-1=0 equation:

46q^2-45q-1=0

a = 46; b = -45; c = -1;
Δ = b2-4ac
Δ = -452-4·46·(-1)
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-47}{2*46}=\frac{-2}{92}
=-1/46
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+47}{2*46}=\frac{92}{92}
=1
$