5/4t-2=3/2t-4

Solution for 5/4t-2=3/2t-4 equation:

5/4t-2=3/2t-4

We move all terms to the left:

5/4t-2-(3/2t-4)=0


Domain of the equation: 4t!=0

t!=0/4

t!=0

t∈R



Domain of the equation: 2t-4)!=0

t∈R


We get rid of parentheses

5/4t-3/2t+4-2=0

We calculate fractions


10t/8t^2+(-12t)/8t^2+4-2=0

We add all the numbers together, and all the variables

10t/8t^2+(-12t)/8t^2+2=0

We multiply all the terms by the denominator


10t+(-12t)+2*8t^2=0

Wy multiply elements

16t^2+10t+(-12t)=0

We get rid of parentheses

16t^2+10t-12t=0

We add all the numbers together, and all the variables

16t^2-2t=0

a = 16; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·16·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*16}=\frac{0}{32}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*16}=\frac{4}{32}
=1/8
$