5k^2+13k=46

Solution for 5k^2+13k=46 equation:

5k^2+13k=46

We move all terms to the left:

5k^2+13k-(46)=0

a = 5; b = 13; c = -46;
Δ = b2-4ac
Δ = 132-4·5·(-46)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-33}{2*5}=\frac{-46}{10}
=-4+3/5
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+33}{2*5}=\frac{20}{10}
=2
$