-32a^2+51a-18=0

Solution for -32a^2+51a-18=0 equation:

-32a^2+51a-18=0

a = -32; b = 51; c = -18;
Δ = b2-4ac
Δ = 512-4·(-32)·(-18)
Δ = 297
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-3\sqrt{33}}{2*-32}=\frac{-51-3\sqrt{33}}{-64}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+3\sqrt{33}}{2*-32}=\frac{-51+3\sqrt{33}}{-64}
$