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6x^2-47x+77=0
a = 6; b = -47; c = +77;
Δ = b2-4ac
Δ = -472-4·6·77
Δ = 361
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{361}=19$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-19}{2*6}=\frac{28}{12} =2+1/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+19}{2*6}=\frac{66}{12} =5+1/2 $
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