12a^2-a-46=0

Solution for 12a^2-a-46=0 equation:

12a^2-a-46=0

We add all the numbers together, and all the variables

12a^2-1a-46=0

a = 12; b = -1; c = -46;
Δ = b2-4ac
Δ = -12-4·12·(-46)
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-47}{2*12}=\frac{-46}{24}
=-1+11/12
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+47}{2*12}=\frac{48}{24}
=2
$