8c2+7c=1

Solution for 8c2+7c=1 equation:

8c^2+7c=1

We move all terms to the left:

8c^2+7c-(1)=0

a = 8; b = 7; c = -1;
Δ = b2-4ac
Δ = 72-4·8·(-1)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-9}{2*8}=\frac{-16}{16}
=-1
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+9}{2*8}=\frac{2}{16}
=1/8
$