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3x^2-38x+55=0
a = 3; b = -38; c = +55;
Δ = b2-4ac
Δ = -382-4·3·55
Δ = 784
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{784}=28$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-28}{2*3}=\frac{10}{6} =1+2/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+28}{2*3}=\frac{66}{6} =11 $
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