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.5x^2+15x-9500=0
a = .5; b = 15; c = -9500;
Δ = b2-4ac
Δ = 152-4·.5·(-9500)
Δ = 19225
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{19225}=\sqrt{25*769}=\sqrt{25}*\sqrt{769}=5\sqrt{769}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-5\sqrt{769}}{2*.5}=\frac{-15-5\sqrt{769}}{1} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+5\sqrt{769}}{2*.5}=\frac{-15+5\sqrt{769}}{1} $
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