3k^2-25k=-42

Solution for 3k^2-25k=-42 equation:

3k^2-25k=-42

We move all terms to the left:

3k^2-25k-(-42)=0

We add all the numbers together, and all the variables

3k^2-25k+42=0

a = 3; b = -25; c = +42;
Δ = b2-4ac
Δ = -252-4·3·42
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-11}{2*3}=\frac{14}{6}
=2+1/3
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+11}{2*3}=\frac{36}{6}
=6
$