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12x^2-77x+30=0
a = 12; b = -77; c = +30;
Δ = b2-4ac
Δ = -772-4·12·30
Δ = 4489
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{4489}=67$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-77)-67}{2*12}=\frac{10}{24} =5/12 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-77)+67}{2*12}=\frac{144}{24} =6 $
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