3/4t+2=5/8t-2

Solution for 3/4t+2=5/8t-2 equation:

3/4t+2=5/8t-2

We move all terms to the left:

3/4t+2-(5/8t-2)=0


Domain of the equation: 4t!=0

t!=0/4

t!=0

t∈R



Domain of the equation: 8t-2)!=0

t∈R


We get rid of parentheses

3/4t-5/8t+2+2=0

We calculate fractions


24t/32t^2+(-20t)/32t^2+2+2=0

We add all the numbers together, and all the variables

24t/32t^2+(-20t)/32t^2+4=0

We multiply all the terms by the denominator


24t+(-20t)+4*32t^2=0

Wy multiply elements

128t^2+24t+(-20t)=0

We get rid of parentheses

128t^2+24t-20t=0

We add all the numbers together, and all the variables

128t^2+4t=0

a = 128; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·128·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*128}=\frac{-8}{256}
=-1/32
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*128}=\frac{0}{256}
=0
$