2=1.5+t(30-4.9t)

Solution for 2=1.5+t(30-4.9t) equation:

2=1.5+t(30-4.9t)

We move all terms to the left:

2-(1.5+t(30-4.9t))=0

We add all the numbers together, and all the variables

-(1.5+t(-4.9t+30))+2=0


We calculate terms in parentheses: -(1.5+t(-4.9t+30)), so:

1.5+t(-4.9t+30)

determiningTheFunctionDomain
t(-4.9t+30)+1.5

We multiply parentheses

-4t^2+30t+1.5

Back to the equation:

-(-4t^2+30t+1.5)


We get rid of parentheses

4t^2-30t-1.5+2=0

We add all the numbers together, and all the variables

4t^2-30t+0.5=0

a = 4; b = -30; c = +0.5;
Δ = b2-4ac
Δ = -302-4·4·0.5
Δ = 892
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:

$\sqrt{\Delta}=\sqrt{892}=\sqrt{4*223}=\sqrt{4}*\sqrt{223}=2\sqrt{223}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{223}}{2*4}=\frac{30-2\sqrt{223}}{8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{223}}{2*4}=\frac{30+2\sqrt{223}}{8}
$