10k(k-2)=7k-4

Solution for 10k(k-2)=7k-4 equation:

10k(k-2)=7k-4

We move all terms to the left:

10k(k-2)-(7k-4)=0

We multiply parentheses

10k^2-20k-(7k-4)=0

We get rid of parentheses

10k^2-20k-7k+4=0

We add all the numbers together, and all the variables

10k^2-27k+4=0

a = 10; b = -27; c = +4;
Δ = b2-4ac
Δ = -272-4·10·4
Δ = 569
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-\sqrt{569}}{2*10}=\frac{27-\sqrt{569}}{20}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{569}}{2*10}=\frac{27+\sqrt{569}}{20}
$