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8x^2-57x-743=0
a = 8; b = -57; c = -743;
Δ = b2-4ac
Δ = -572-4·8·(-743)
Δ = 27025
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{27025}=\sqrt{25*1081}=\sqrt{25}*\sqrt{1081}=5\sqrt{1081}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-57)-5\sqrt{1081}}{2*8}=\frac{57-5\sqrt{1081}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-57)+5\sqrt{1081}}{2*8}=\frac{57+5\sqrt{1081}}{16} $
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