5+31/2t=6+21/4t

Solution for 5+31/2t=6+21/4t equation:

5+31/2t=6+21/4t

We move all terms to the left:

5+31/2t-(6+21/4t)=0


Domain of the equation: 2t!=0

t!=0/2

t!=0

t∈R



Domain of the equation: 4t)!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

31/2t-(21/4t+6)+5=0

We get rid of parentheses

31/2t-21/4t-6+5=0

We calculate fractions


124t/8t^2+(-42t)/8t^2-6+5=0

We add all the numbers together, and all the variables

124t/8t^2+(-42t)/8t^2-1=0

We multiply all the terms by the denominator


124t+(-42t)-1*8t^2=0

Wy multiply elements

-8t^2+124t+(-42t)=0

We get rid of parentheses

-8t^2+124t-42t=0

We add all the numbers together, and all the variables

-8t^2+82t=0

a = -8; b = 82; c = 0;
Δ = b2-4ac
Δ = 822-4·(-8)·0
Δ = 6724
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6724}=82$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(82)-82}{2*-8}=\frac{-164}{-16}
=10+1/4
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(82)+82}{2*-8}=\frac{0}{-16}
=0
$