4a^2-a-9=0

Solution for 4a^2-a-9=0 equation:

4a^2-a-9=0

We add all the numbers together, and all the variables

4a^2-1a-9=0

a = 4; b = -1; c = -9;
Δ = b2-4ac
Δ = -12-4·4·(-9)
Δ = 145
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{145}}{2*4}=\frac{1-\sqrt{145}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{145}}{2*4}=\frac{1+\sqrt{145}}{8}
$