3k^2+13k=-10

Solution for 3k^2+13k=-10 equation:

3k^2+13k=-10

We move all terms to the left:

3k^2+13k-(-10)=0

We add all the numbers together, and all the variables

3k^2+13k+10=0

a = 3; b = 13; c = +10;
Δ = b2-4ac
Δ = 132-4·3·10
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-7}{2*3}=\frac{-20}{6}
=-3+1/3
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+7}{2*3}=\frac{-6}{6}
=-1
$