4b^2-b=9

Solution for 4b^2-b=9 equation:

4b^2-b=9

We move all terms to the left:

4b^2-b-(9)=0

We add all the numbers together, and all the variables

4b^2-1b-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:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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