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-x^2+24x-60=0
We add all the numbers together, and all the variables
-1x^2+24x-60=0
a = -1; b = 24; c = -60;
Δ = b2-4ac
Δ = 242-4·(-1)·(-60)
Δ = 336
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{21}}{2*-1}=\frac{-24-4\sqrt{21}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{21}}{2*-1}=\frac{-24+4\sqrt{21}}{-2} $
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