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-4x^2+160x+1600=0
a = -4; b = 160; c = +1600;
Δ = b2-4ac
Δ = 1602-4·(-4)·1600
Δ = 51200
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{51200}=\sqrt{25600*2}=\sqrt{25600}*\sqrt{2}=160\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-160\sqrt{2}}{2*-4}=\frac{-160-160\sqrt{2}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+160\sqrt{2}}{2*-4}=\frac{-160+160\sqrt{2}}{-8} $
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