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12t+36=6t^2+24t
We move all terms to the left:
12t+36-(6t^2+24t)=0
We get rid of parentheses
-6t^2+12t-24t+36=0
We add all the numbers together, and all the variables
-6t^2-12t+36=0
a = -6; b = -12; c = +36;
Δ = b2-4ac
Δ = -122-4·(-6)·36
Δ = 1008
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}$$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{7}}{2*-6}=\frac{12-12\sqrt{7}}{-12} $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{7}}{2*-6}=\frac{12+12\sqrt{7}}{-12} $
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