8c^2-18c=23

Solution for 8c^2-18c=23 equation:

8c^2-18c=23

We move all terms to the left:

8c^2-18c-(23)=0

a = 8; b = -18; c = -23;
Δ = b2-4ac
Δ = -182-4·8·(-23)
Δ = 1060
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1060}=\sqrt{4*265}=\sqrt{4}*\sqrt{265}=2\sqrt{265}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{265}}{2*8}=\frac{18-2\sqrt{265}}{16}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{265}}{2*8}=\frac{18+2\sqrt{265}}{16}
$