2b^2-46b+16=0

Solution for 2b^2-46b+16=0 equation:

2b^2-46b+16=0

a = 2; b = -46; c = +16;
Δ = b2-4ac
Δ = -462-4·2·16
Δ = 1988
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:

$\sqrt{\Delta}=\sqrt{1988}=\sqrt{4*497}=\sqrt{4}*\sqrt{497}=2\sqrt{497}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-2\sqrt{497}}{2*2}=\frac{46-2\sqrt{497}}{4}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+2\sqrt{497}}{2*2}=\frac{46+2\sqrt{497}}{4}
$