X^2-0.8x-0.16=10

Solution for X^2-0.8x-0.16=10 equation:

X^2-0.8X-0.16=10

We move all terms to the left:

X^2-0.8X-0.16-(10)=0

We add all the numbers together, and all the variables

X^2-0.8X-10.16=0

a = 1; b = -0.8; c = -10.16;
Δ = b2-4ac
Δ = -0.82-4·1·(-10.16)
Δ = 41.28
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-0.8)-\sqrt{41.28}}{2*1}=\frac{0.8-\sqrt{41.28}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.8)+\sqrt{41.28}}{2*1}=\frac{0.8+\sqrt{41.28}}{2}
$