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24x^2-66x+45=0
a = 24; b = -66; c = +45;
Δ = b2-4ac
Δ = -662-4·24·45
Δ = 36
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{36}=6$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-6}{2*24}=\frac{60}{48} =1+1/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+6}{2*24}=\frac{72}{48} =1+1/2 $
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