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14x^2+11x-40=0
a = 14; b = 11; c = -40;
Δ = b2-4ac
Δ = 112-4·14·(-40)
Δ = 2361
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{-(11)-\sqrt{2361}}{2*14}=\frac{-11-\sqrt{2361}}{28} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{2361}}{2*14}=\frac{-11+\sqrt{2361}}{28} $
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