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5x^2-11x-102=0
a = 5; b = -11; c = -102;
Δ = b2-4ac
Δ = -112-4·5·(-102)
Δ = 2161
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{2161}}{2*5}=\frac{11-\sqrt{2161}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{2161}}{2*5}=\frac{11+\sqrt{2161}}{10} $
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