(-10k+7)(-2k+6)=0

Solution for (-10k+7)(-2k+6)=0 equation:

(-10k+7)(-2k+6)=0

We multiply parentheses ..

(+20k^2-60k-14k+42)=0

We get rid of parentheses

20k^2-60k-14k+42=0

We add all the numbers together, and all the variables

20k^2-74k+42=0

a = 20; b = -74; c = +42;
Δ = b2-4ac
Δ = -742-4·20·42
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-74)-46}{2*20}=\frac{28}{40}
=7/10
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-74)+46}{2*20}=\frac{120}{40}
=3
$