4a^2-8a-39=0

Solution for 4a^2-8a-39=0 equation:

4a^2-8a-39=0

a = 4; b = -8; c = -39;
Δ = b2-4ac
Δ = -82-4·4·(-39)
Δ = 688
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:

$\sqrt{\Delta}=\sqrt{688}=\sqrt{16*43}=\sqrt{16}*\sqrt{43}=4\sqrt{43}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{43}}{2*4}=\frac{8-4\sqrt{43}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{43}}{2*4}=\frac{8+4\sqrt{43}}{8}
$