20b^2-15b=18

Solution for 20b^2-15b=18 equation:

20b^2-15b=18

We move all terms to the left:

20b^2-15b-(18)=0

a = 20; b = -15; c = -18;
Δ = b2-4ac
Δ = -152-4·20·(-18)
Δ = 1665
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:

$\sqrt{\Delta}=\sqrt{1665}=\sqrt{9*185}=\sqrt{9}*\sqrt{185}=3\sqrt{185}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{185}}{2*20}=\frac{15-3\sqrt{185}}{40}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{185}}{2*20}=\frac{15+3\sqrt{185}}{40}
$