7k^2+31k+30=0

Solution for 7k^2+31k+30=0 equation:

7k^2+31k+30=0

a = 7; b = 31; c = +30;
Δ = b2-4ac
Δ = 312-4·7·30
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{-(31)-11}{2*7}=\frac{-42}{14}
=-3
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+11}{2*7}=\frac{-20}{14}
=-1+3/7
$