4(2b^2-b-45)=0

Solution for 4(2b^2-b-45)=0 equation:

4(2b^2-b-45)=0

We multiply parentheses

8b^2-4b-180=0

a = 8; b = -4; c = -180;
Δ = b2-4ac
Δ = -42-4·8·(-180)
Δ = 5776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5776}=76$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-76}{2*8}=\frac{-72}{16}
=-4+1/2
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+76}{2*8}=\frac{80}{16}
=5
$