4a^2+4a-23=0

Solution for 4a^2+4a-23=0 equation:

4a^2+4a-23=0

a = 4; b = 4; c = -23;
Δ = b2-4ac
Δ = 42-4·4·(-23)
Δ = 384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8\sqrt{6}}{2*4}=\frac{-4-8\sqrt{6}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8\sqrt{6}}{2*4}=\frac{-4+8\sqrt{6}}{8}
$