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-1.0477x^2+38.9047x-349.8572=0
a = -1.0477; b = 38.9047; c = -349.8572;
Δ = b2-4ac
Δ = 38.90472-4·(-1.0477)·(-349.8572)
Δ = 47.39412833
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38.9047)-\sqrt{47.39412833}}{2*-1.0477}=\frac{-38.9047-\sqrt{47.39412833}}{-2.0954} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38.9047)+\sqrt{47.39412833}}{2*-1.0477}=\frac{-38.9047+\sqrt{47.39412833}}{-2.0954} $
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