-8x^2-10x+2=0

Solution for -8x^2-10x+2=0 equation:

-8x^2-10x+2=0

a = -8; b = -10; c = +2;
Δ = b2-4ac
Δ = -102-4·(-8)·2
Δ = 164
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:

$\sqrt{\Delta}=\sqrt{164}=\sqrt{4*41}=\sqrt{4}*\sqrt{41}=2\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{41}}{2*-8}=\frac{10-2\sqrt{41}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{41}}{2*-8}=\frac{10+2\sqrt{41}}{-16}
$