X=16t^2+64t+60

Solution for X=16t^2+64t+60 equation:

X=16X^2+64X+60

We move all terms to the left:

X-(16X^2+64X+60)=0

We get rid of parentheses

-16X^2+X-64X-60=0

We add all the numbers together, and all the variables

-16X^2-63X-60=0

a = -16; b = -63; c = -60;
Δ = b2-4ac
Δ = -632-4·(-16)·(-60)
Δ = 129
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{-(-63)-\sqrt{129}}{2*-16}=\frac{63-\sqrt{129}}{-32}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+\sqrt{129}}{2*-16}=\frac{63+\sqrt{129}}{-32}
$