(-10k+10)(-8k+10)=0

Solution for (-10k+10)(-8k+10)=0 equation:

(-10k+10)(-8k+10)=0

We multiply parentheses ..

(+80k^2-100k-80k+100)=0

We get rid of parentheses

80k^2-100k-80k+100=0

We add all the numbers together, and all the variables

80k^2-180k+100=0

a = 80; b = -180; c = +100;
Δ = b2-4ac
Δ = -1802-4·80·100
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-20}{2*80}=\frac{160}{160}
=1
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+20}{2*80}=\frac{200}{160}
=1+1/4
$