(k-5)(8k-3)=0

Solution for (k-5)(8k-3)=0 equation:

(k-5)(8k-3)=0

We multiply parentheses ..

(+8k^2-3k-40k+15)=0

We get rid of parentheses

8k^2-3k-40k+15=0

We add all the numbers together, and all the variables

8k^2-43k+15=0

a = 8; b = -43; c = +15;
Δ = b2-4ac
Δ = -432-4·8·15
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-43)-37}{2*8}=\frac{6}{16}
=3/8
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+37}{2*8}=\frac{80}{16}
=5
$