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12x^2-45x+20=0
a = 12; b = -45; c = +20;
Δ = b2-4ac
Δ = -452-4·12·20
Δ = 1065
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-\sqrt{1065}}{2*12}=\frac{45-\sqrt{1065}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{1065}}{2*12}=\frac{45+\sqrt{1065}}{24} $
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