16b^2-72b+81=43

Solution for 16b^2-72b+81=43 equation:

16b^2-72b+81=43

We move all terms to the left:

16b^2-72b+81-(43)=0

We add all the numbers together, and all the variables

16b^2-72b+38=0

a = 16; b = -72; c = +38;
Δ = b2-4ac
Δ = -722-4·16·38
Δ = 2752
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:

$\sqrt{\Delta}=\sqrt{2752}=\sqrt{64*43}=\sqrt{64}*\sqrt{43}=8\sqrt{43}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-8\sqrt{43}}{2*16}=\frac{72-8\sqrt{43}}{32}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+8\sqrt{43}}{2*16}=\frac{72+8\sqrt{43}}{32}
$