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17x^2+48x+9=0
a = 17; b = 48; c = +9;
Δ = b2-4ac
Δ = 482-4·17·9
Δ = 1692
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1692}=\sqrt{36*47}=\sqrt{36}*\sqrt{47}=6\sqrt{47}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-6\sqrt{47}}{2*17}=\frac{-48-6\sqrt{47}}{34} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+6\sqrt{47}}{2*17}=\frac{-48+6\sqrt{47}}{34} $
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