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-5x^2+97x+102=0
a = -5; b = 97; c = +102;
Δ = b2-4ac
Δ = 972-4·(-5)·102
Δ = 11449
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{11449}=107$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(97)-107}{2*-5}=\frac{-204}{-10} =20+2/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(97)+107}{2*-5}=\frac{10}{-10} =-1 $
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