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x^2-47x-68=0
a = 1; b = -47; c = -68;
Δ = b2-4ac
Δ = -472-4·1·(-68)
Δ = 2481
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{-(-47)-\sqrt{2481}}{2*1}=\frac{47-\sqrt{2481}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+\sqrt{2481}}{2*1}=\frac{47+\sqrt{2481}}{2} $
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