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48x^2-208x+9=0
a = 48; b = -208; c = +9;
Δ = b2-4ac
Δ = -2082-4·48·9
Δ = 41536
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{41536}=\sqrt{64*649}=\sqrt{64}*\sqrt{649}=8\sqrt{649}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-208)-8\sqrt{649}}{2*48}=\frac{208-8\sqrt{649}}{96} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-208)+8\sqrt{649}}{2*48}=\frac{208+8\sqrt{649}}{96} $
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