8r2-10r-10=0

Solution for 8r2-10r-10=0 equation:

8r^2-10r-10=0

a = 8; b = -10; c = -10;
Δ = b2-4ac
Δ = -102-4·8·(-10)
Δ = 420
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{105}}{2*8}=\frac{10-2\sqrt{105}}{16}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{105}}{2*8}=\frac{10+2\sqrt{105}}{16}
$