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85x^2-24x-45=0
a = 85; b = -24; c = -45;
Δ = b2-4ac
Δ = -242-4·85·(-45)
Δ = 15876
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{15876}=126$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-126}{2*85}=\frac{-102}{170} =-3/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+126}{2*85}=\frac{150}{170} =15/17 $
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