10k(k-3)=7k-12

Solution for 10k(k-3)=7k-12 equation:

10k(k-3)=7k-12

We move all terms to the left:

10k(k-3)-(7k-12)=0

We multiply parentheses

10k^2-30k-(7k-12)=0

We get rid of parentheses

10k^2-30k-7k+12=0

We add all the numbers together, and all the variables

10k^2-37k+12=0

a = 10; b = -37; c = +12;
Δ = b2-4ac
Δ = -372-4·10·12
Δ = 889
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{-(-37)-\sqrt{889}}{2*10}=\frac{37-\sqrt{889}}{20}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+\sqrt{889}}{2*10}=\frac{37+\sqrt{889}}{20}
$