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24t=15+6t^2
We move all terms to the left:
24t-(15+6t^2)=0
We get rid of parentheses
-6t^2+24t-15=0
a = -6; b = 24; c = -15;
Δ = b2-4ac
Δ = 242-4·(-6)·(-15)
Δ = 216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-6\sqrt{6}}{2*-6}=\frac{-24-6\sqrt{6}}{-12} $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+6\sqrt{6}}{2*-6}=\frac{-24+6\sqrt{6}}{-12} $
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