8a^2-16a-71=-7

Solution for 8a^2-16a-71=-7 equation:

8a^2-16a-71=-7

We move all terms to the left:

8a^2-16a-71-(-7)=0

We add all the numbers together, and all the variables

8a^2-16a-64=0

a = 8; b = -16; c = -64;
Δ = b2-4ac
Δ = -162-4·8·(-64)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-48}{2*8}=\frac{-32}{16}
=-2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+48}{2*8}=\frac{64}{16}
=4
$