1800=1/2(5)t^2

Solution for 1800=1/2(5)t^2 equation:

1800=1/2(5)t^2

We move all terms to the left:

1800-(1/2(5)t^2)=0


Domain of the equation: 25t^2)!=0

t!=0/1

t!=0

t∈R


We get rid of parentheses

-1/25t^2+1800=0

We multiply all the terms by the denominator


1800*25t^2-1=0

Wy multiply elements

45000t^2-1=0

a = 45000; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·45000·(-1)
Δ = 180000
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:

$\sqrt{\Delta}=\sqrt{180000}=\sqrt{90000*2}=\sqrt{90000}*\sqrt{2}=300\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-300\sqrt{2}}{2*45000}=\frac{0-300\sqrt{2}}{90000}
=-\frac{300\sqrt{2}}{90000}
=-\frac{\sqrt{2}}{300}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+300\sqrt{2}}{2*45000}=\frac{0+300\sqrt{2}}{90000}
=\frac{300\sqrt{2}}{90000}
=\frac{\sqrt{2}}{300}
$