3-2/9t=1/3t-7

Solution for 3-2/9t=1/3t-7 equation:

3-2/9t=1/3t-7

We move all terms to the left:

3-2/9t-(1/3t-7)=0


Domain of the equation: 9t!=0

t!=0/9

t!=0

t∈R



Domain of the equation: 3t-7)!=0

t∈R


We get rid of parentheses

-2/9t-1/3t+7+3=0

We calculate fractions


(-6t)/27t^2+(-9t)/27t^2+7+3=0

We add all the numbers together, and all the variables

(-6t)/27t^2+(-9t)/27t^2+10=0

We multiply all the terms by the denominator


(-6t)+(-9t)+10*27t^2=0

Wy multiply elements

270t^2+(-6t)+(-9t)=0

We get rid of parentheses

270t^2-6t-9t=0

We add all the numbers together, and all the variables

270t^2-15t=0

a = 270; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·270·0
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*270}=\frac{0}{540}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*270}=\frac{30}{540}
=1/18
$