8x^2-8x-105=0

Solution for 8x^2-8x-105=0 equation:

8x^2-8x-105=0

a = 8; b = -8; c = -105;
Δ = b2-4ac
Δ = -82-4·8·(-105)
Δ = 3424
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3424}=\sqrt{16*214}=\sqrt{16}*\sqrt{214}=4\sqrt{214}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{214}}{2*8}=\frac{8-4\sqrt{214}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{214}}{2*8}=\frac{8+4\sqrt{214}}{16}
$