2b^2+14b+23=0

Solution for 2b^2+14b+23=0 equation:

2b^2+14b+23=0

a = 2; b = 14; c = +23;
Δ = b2-4ac
Δ = 142-4·2·23
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{3}}{2*2}=\frac{-14-2\sqrt{3}}{4}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{3}}{2*2}=\frac{-14+2\sqrt{3}}{4}
$