k(8k-7)=0

Solution for k(8k-7)=0 equation:

k(8k-7)=0

We multiply parentheses

8k^2-7k=0

a = 8; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·8·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*8}=\frac{0}{16}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*8}=\frac{14}{16}
=7/8
$