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48x^2+5x-108000=0
a = 48; b = 5; c = -108000;
Δ = b2-4ac
Δ = 52-4·48·(-108000)
Δ = 20736025
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{20736025}=\sqrt{25*829441}=\sqrt{25}*\sqrt{829441}=5\sqrt{829441}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{829441}}{2*48}=\frac{-5-5\sqrt{829441}}{96} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{829441}}{2*48}=\frac{-5+5\sqrt{829441}}{96} $
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