25k^2=12-5k

Solution for 25k^2=12-5k equation:

25k^2=12-5k

We move all terms to the left:

25k^2-(12-5k)=0

We add all the numbers together, and all the variables

25k^2-(-5k+12)=0

We get rid of parentheses

25k^2+5k-12=0

a = 25; b = 5; c = -12;
Δ = b2-4ac
Δ = 52-4·25·(-12)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-35}{2*25}=\frac{-40}{50}
=-4/5
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+35}{2*25}=\frac{30}{50}
=3/5
$