4a^2-8a-23=2

Solution for 4a^2-8a-23=2 equation:

4a^2-8a-23=2

We move all terms to the left:

4a^2-8a-23-(2)=0

We add all the numbers together, and all the variables

4a^2-8a-25=0

a = 4; b = -8; c = -25;
Δ = b2-4ac
Δ = -82-4·4·(-25)
Δ = 464
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:

$\sqrt{\Delta}=\sqrt{464}=\sqrt{16*29}=\sqrt{16}*\sqrt{29}=4\sqrt{29}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{29}}{2*4}=\frac{8-4\sqrt{29}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{29}}{2*4}=\frac{8+4\sqrt{29}}{8}
$