8b2-18b+3=0

Solution for 8b2-18b+3=0 equation:

8b^2-18b+3=0

a = 8; b = -18; c = +3;
Δ = b2-4ac
Δ = -182-4·8·3
Δ = 228
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{57}}{2*8}=\frac{18-2\sqrt{57}}{16}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{57}}{2*8}=\frac{18+2\sqrt{57}}{16}
$