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17x^2+52x+3=0
a = 17; b = 52; c = +3;
Δ = b2-4ac
Δ = 522-4·17·3
Δ = 2500
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{2500}=50$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-50}{2*17}=\frac{-102}{34} =-3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+50}{2*17}=\frac{-2}{34} =-1/17 $
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