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24x^2-90x+66=0
a = 24; b = -90; c = +66;
Δ = b2-4ac
Δ = -902-4·24·66
Δ = 1764
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{1764}=42$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-42}{2*24}=\frac{48}{48} =1 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+42}{2*24}=\frac{132}{48} =2+3/4 $
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