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5x^2-48x-10800=0
a = 5; b = -48; c = -10800;
Δ = b2-4ac
Δ = -482-4·5·(-10800)
Δ = 218304
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{218304}=\sqrt{576*379}=\sqrt{576}*\sqrt{379}=24\sqrt{379}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-24\sqrt{379}}{2*5}=\frac{48-24\sqrt{379}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+24\sqrt{379}}{2*5}=\frac{48+24\sqrt{379}}{10} $
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