3/4t-2/3t=5/6

Solution for 3/4t-2/3t=5/6 equation:

3/4t-2/3t=5/6

We move all terms to the left:

3/4t-2/3t-(5/6)=0


Domain of the equation: 4t!=0

t!=0/4

t!=0

t∈R



Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R


We add all the numbers together, and all the variables

3/4t-2/3t-(+5/6)=0

We get rid of parentheses

3/4t-2/3t-5/6=0

We calculate fractions


(-180t^2)/432t^2+324t/432t^2+(-288t)/432t^2=0

We multiply all the terms by the denominator


(-180t^2)+324t+(-288t)=0

We get rid of parentheses

-180t^2+324t-288t=0

We add all the numbers together, and all the variables

-180t^2+36t=0

a = -180; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-180)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*-180}=\frac{-72}{-360}
=1/5
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-180}=\frac{0}{-360}
=0
$