25k^2=60k-32

Solution for 25k^2=60k-32 equation:

25k^2=60k-32

We move all terms to the left:

25k^2-(60k-32)=0

We get rid of parentheses

25k^2-60k+32=0

a = 25; b = -60; c = +32;
Δ = b2-4ac
Δ = -602-4·25·32
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-20}{2*25}=\frac{40}{50}
=4/5
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+20}{2*25}=\frac{80}{50}
=1+3/5
$