(5/4)t=45/2

Solution for (5/4)t=45/2 equation:

(5/4)t=45/2

We move all terms to the left:

(5/4)t-(45/2)=0


Domain of the equation: 4)t!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

(+5/4)t-(+45/2)=0

We multiply parentheses

5t^2-(+45/2)=0

We get rid of parentheses

5t^2-45/2=0

We multiply all the terms by the denominator


5t^2*2-45=0

Wy multiply elements

10t^2-45=0

a = 10; b = 0; c = -45;
Δ = b2-4ac
Δ = 02-4·10·(-45)
Δ = 1800
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:

$\sqrt{\Delta}=\sqrt{1800}=\sqrt{900*2}=\sqrt{900}*\sqrt{2}=30\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{2}}{2*10}=\frac{0-30\sqrt{2}}{20}
=-\frac{30\sqrt{2}}{20}
=-\frac{3\sqrt{2}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{2}}{2*10}=\frac{0+30\sqrt{2}}{20}
=\frac{30\sqrt{2}}{20}
=\frac{3\sqrt{2}}{2}
$