7k2+57k+13=5

Solution for 7k2+57k+13=5 equation:

7k^2+57k+13=5

We move all terms to the left:

7k^2+57k+13-(5)=0

We add all the numbers together, and all the variables

7k^2+57k+8=0

a = 7; b = 57; c = +8;
Δ = b2-4ac
Δ = 572-4·7·8
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(57)-55}{2*7}=\frac{-112}{14}
=-8
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(57)+55}{2*7}=\frac{-2}{14}
=-1/7
$