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24x^2+162x-4=0
a = 24; b = 162; c = -4;
Δ = b2-4ac
Δ = 1622-4·24·(-4)
Δ = 26628
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{26628}=\sqrt{4*6657}=\sqrt{4}*\sqrt{6657}=2\sqrt{6657}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(162)-2\sqrt{6657}}{2*24}=\frac{-162-2\sqrt{6657}}{48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(162)+2\sqrt{6657}}{2*24}=\frac{-162+2\sqrt{6657}}{48} $
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