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32a^2-60a+27=0
a = 32; b = -60; c = +27;
Δ = b2-4ac
Δ = -602-4·32·27
Δ = 144
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}$$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{144}=12$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-12}{2*32}=\frac{48}{64} =3/4 $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+12}{2*32}=\frac{72}{64} =1+1/8 $
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