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96x^2-585x+30=0
a = 96; b = -585; c = +30;
Δ = b2-4ac
Δ = -5852-4·96·30
Δ = 330705
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{330705}=\sqrt{9*36745}=\sqrt{9}*\sqrt{36745}=3\sqrt{36745}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-585)-3\sqrt{36745}}{2*96}=\frac{585-3\sqrt{36745}}{192} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-585)+3\sqrt{36745}}{2*96}=\frac{585+3\sqrt{36745}}{192} $
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