8k^2+26k=3

Solution for 8k^2+26k=3 equation:

8k^2+26k=3

We move all terms to the left:

8k^2+26k-(3)=0

a = 8; b = 26; c = -3;
Δ = b2-4ac
Δ = 262-4·8·(-3)
Δ = 772
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{772}=\sqrt{4*193}=\sqrt{4}*\sqrt{193}=2\sqrt{193}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{193}}{2*8}=\frac{-26-2\sqrt{193}}{16}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{193}}{2*8}=\frac{-26+2\sqrt{193}}{16}
$