18b2-54b=40

Solution for 18b2-54b=40 equation:

18b^2-54b=40

We move all terms to the left:

18b^2-54b-(40)=0

a = 18; b = -54; c = -40;
Δ = b2-4ac
Δ = -542-4·18·(-40)
Δ = 5796
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:

$\sqrt{\Delta}=\sqrt{5796}=\sqrt{36*161}=\sqrt{36}*\sqrt{161}=6\sqrt{161}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6\sqrt{161}}{2*18}=\frac{54-6\sqrt{161}}{36}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6\sqrt{161}}{2*18}=\frac{54+6\sqrt{161}}{36}
$