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85x^2-74x-115=0
a = 85; b = -74; c = -115;
Δ = b2-4ac
Δ = -742-4·85·(-115)
Δ = 44576
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{44576}=\sqrt{16*2786}=\sqrt{16}*\sqrt{2786}=4\sqrt{2786}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-74)-4\sqrt{2786}}{2*85}=\frac{74-4\sqrt{2786}}{170} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-74)+4\sqrt{2786}}{2*85}=\frac{74+4\sqrt{2786}}{170} $
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