8k^2+3k=1

Solution for 8k^2+3k=1 equation:

8k^2+3k=1

We move all terms to the left:

8k^2+3k-(1)=0

a = 8; b = 3; c = -1;
Δ = b2-4ac
Δ = 32-4·8·(-1)
Δ = 41
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{41}}{2*8}=\frac{-3-\sqrt{41}}{16}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{41}}{2*8}=\frac{-3+\sqrt{41}}{16}
$