X=-3t^2+12t+5

Solution for X=-3t^2+12t+5 equation:

X=-3X^2+12X+5

We move all terms to the left:

X-(-3X^2+12X+5)=0

We get rid of parentheses

3X^2-12X+X-5=0

We add all the numbers together, and all the variables

3X^2-11X-5=0

a = 3; b = -11; c = -5;
Δ = b2-4ac
Δ = -112-4·3·(-5)
Δ = 181
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{181}}{2*3}=\frac{11-\sqrt{181}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{181}}{2*3}=\frac{11+\sqrt{181}}{6}
$