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12x^2-47x+45=0
a = 12; b = -47; c = +45;
Δ = b2-4ac
Δ = -472-4·12·45
Δ = 49
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{49}=7$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-7}{2*12}=\frac{40}{24} =1+2/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+7}{2*12}=\frac{54}{24} =2+1/4 $
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