4b^2+20b+23=0

Solution for 4b^2+20b+23=0 equation:

4b^2+20b+23=0

a = 4; b = 20; c = +23;
Δ = b2-4ac
Δ = 202-4·4·23
Δ = 32
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{2}}{2*4}=\frac{-20-4\sqrt{2}}{8}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{2}}{2*4}=\frac{-20+4\sqrt{2}}{8}
$