45=1/2*10t^2

Solution for 45=1/2*10t^2 equation:

45=1/2*10t^2

We move all terms to the left:

45-(1/2*10t^2)=0


Domain of the equation: 2*10t^2)!=0

t!=0/1

t!=0

t∈R


We get rid of parentheses

-1/2*10t^2+45=0

We multiply all the terms by the denominator


45*2*10t^2-1=0

Wy multiply elements

900t^2*1-1=0

Wy multiply elements

900t^2-1=0

a = 900; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·900·(-1)
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60}{2*900}=\frac{-60}{1800}
=-1/30
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60}{2*900}=\frac{60}{1800}
=1/30
$