-21b^2-186b+27=0

Solution for -21b^2-186b+27=0 equation:

-21b^2-186b+27=0

a = -21; b = -186; c = +27;
Δ = b2-4ac
Δ = -1862-4·(-21)·27
Δ = 36864
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36864}=192$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-186)-192}{2*-21}=\frac{-6}{-42}
=1/7
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-186)+192}{2*-21}=\frac{378}{-42}
=-9
$