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30x^2-47x+14=0
a = 30; b = -47; c = +14;
Δ = b2-4ac
Δ = -472-4·30·14
Δ = 529
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{529}=23$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-23}{2*30}=\frac{24}{60} =2/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+23}{2*30}=\frac{70}{60} =1+1/6 $
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