Question

Calculate the value of t from the equqtion 5t +1.5t^2=84

Answer 1

5t +1.5t^2=84
multiple by 2 both sides
10t + 3t^2 =168
3t^2 + 10t -168=0
3t^2 -18t +28t -168=0
3t(t-6) +28(t-6)=0
(3t+28) (t-6)=0
3t+28=0. ;. t-6=0
3t= -28. ;. t=6
t= -28/3

Answer 2

Given,

An equation, $5t +1.5t^2=84$

To find,

The value of t.

Solution,

The given equation can be written as follows :

$1.5t^2+5t-84=0$

It is a quadratic equation.

The solution of an equation $ax^2+bx+c=0$ is given by :

$x=\dfrac{-b\pm \sqrt{b^2-4ac} }{2a}$

Using this formula to find the value of t of the given equation :

a = 1.5, b = 5 and c = -84

So,

$t=\dfrac{-5\pm \sqrt{(5)^2-4(1.5)(-84)} }{2(1.5)}\\\\t=\dfrac{-5+ \sqrt{(5)^2-4(1.5)(-84)} }{2(1.5)}, \dfrac{-5- \sqrt{(5)^2-4(1.5)(-84)} }{2(1.5)}\\\\t=6,\dfrac{-28}{3}$

ence, t = 6 and -28/3.