8b^2-36b+19=0

Solution for 8b^2-36b+19=0 equation:

8b^2-36b+19=0

a = 8; b = -36; c = +19;
Δ = b2-4ac
Δ = -362-4·8·19
Δ = 688
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:

$\sqrt{\Delta}=\sqrt{688}=\sqrt{16*43}=\sqrt{16}*\sqrt{43}=4\sqrt{43}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{43}}{2*8}=\frac{36-4\sqrt{43}}{16}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{43}}{2*8}=\frac{36+4\sqrt{43}}{16}
$