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x^2-53.75x-300=0
a = 1; b = -53.75; c = -300;
Δ = b2-4ac
Δ = -53.752-4·1·(-300)
Δ = 4089.0625
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{-(-53.75)-\sqrt{4089.0625}}{2*1}=\frac{53.75-\sqrt{4089.0625}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53.75)+\sqrt{4089.0625}}{2*1}=\frac{53.75+\sqrt{4089.0625}}{2} $
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