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17x^2+40x-400=0
a = 17; b = 40; c = -400;
Δ = b2-4ac
Δ = 402-4·17·(-400)
Δ = 28800
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{28800}=\sqrt{14400*2}=\sqrt{14400}*\sqrt{2}=120\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-120\sqrt{2}}{2*17}=\frac{-40-120\sqrt{2}}{34} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+120\sqrt{2}}{2*17}=\frac{-40+120\sqrt{2}}{34} $
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