9/3t-6=6/0.2t+4

Solution for 9/3t-6=6/0.2t+4 equation:

9/3t-6=6/0.2t+4

We move all terms to the left:

9/3t-6-(6/0.2t+4)=0


Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R



Domain of the equation: 0.2t+4)!=0

t∈R


We get rid of parentheses

9/3t-6/0.2t-4-6=0

We calculate fractions


t/t^2+(-18t)/t^2-4-6=0

We add all the numbers together, and all the variables

t/t^2+(-18t)/t^2-10=0

We multiply all the terms by the denominator


t+(-18t)-10*t^2=0

We add all the numbers together, and all the variables

-10t^2+t+(-18t)=0

We get rid of parentheses

-10t^2+t-18t=0

We add all the numbers together, and all the variables

-10t^2-17t=0

a = -10; b = -17; c = 0;
Δ = b2-4ac
Δ = -172-4·(-10)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-17}{2*-10}=\frac{0}{-20}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+17}{2*-10}=\frac{34}{-20}
=-1+7/10
$