1/9t+14=2/3t

Solution for 1/9t+14=2/3t equation:

1/9t+14=2/3t

We move all terms to the left:

1/9t+14-(2/3t)=0


Domain of the equation: 9t!=0

t!=0/9

t!=0

t∈R



Domain of the equation: 3t)!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

1/9t-(+2/3t)+14=0

We get rid of parentheses

1/9t-2/3t+14=0

We calculate fractions


3t/27t^2+(-18t)/27t^2+14=0

We multiply all the terms by the denominator


3t+(-18t)+14*27t^2=0

Wy multiply elements

378t^2+3t+(-18t)=0

We get rid of parentheses

378t^2+3t-18t=0

We add all the numbers together, and all the variables

378t^2-15t=0

a = 378; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·378·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*378}=\frac{0}{756}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*378}=\frac{30}{756}
=5/126
$