8k^2+13k+1=7

Solution for 8k^2+13k+1=7 equation:

8k^2+13k+1=7

We move all terms to the left:

8k^2+13k+1-(7)=0

We add all the numbers together, and all the variables

8k^2+13k-6=0

a = 8; b = 13; c = -6;
Δ = b2-4ac
Δ = 132-4·8·(-6)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-19}{2*8}=\frac{-32}{16}
=-2
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+19}{2*8}=\frac{6}{16}
=3/8
$