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0=-16x^2+160x+243
We move all terms to the left:
0-(-16x^2+160x+243)=0
We add all the numbers together, and all the variables
-(-16x^2+160x+243)=0
We get rid of parentheses
16x^2-160x-243=0
a = 16; b = -160; c = -243;
Δ = b2-4ac
Δ = -1602-4·16·(-243)
Δ = 41152
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{41152}=\sqrt{64*643}=\sqrt{64}*\sqrt{643}=8\sqrt{643}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-160)-8\sqrt{643}}{2*16}=\frac{160-8\sqrt{643}}{32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-160)+8\sqrt{643}}{2*16}=\frac{160+8\sqrt{643}}{32} $
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