1/3t+7.8-10=-3t+2

Solution for 1/3t+7.8-10=-3t+2 equation:

1/3t+7.8-10=-3t+2

We move all terms to the left:

1/3t+7.8-10-(-3t+2)=0


Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R


We add all the numbers together, and all the variables

1/3t-(-3t+2)-2.2=0

We get rid of parentheses

1/3t+3t-2-2.2=0

We multiply all the terms by the denominator


3t*3t-2*3t-(2.2)*3t+1=0

We multiply parentheses

3t*3t-2*3t-6.6t+1=0

Wy multiply elements

9t^2-6t-6.6t+1=0

We add all the numbers together, and all the variables

9t^2-12.6t+1=0

a = 9; b = -12.6; c = +1;
Δ = b2-4ac
Δ = -12.62-4·9·1
Δ = 122.76
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12.6)-\sqrt{122.76}}{2*9}=\frac{12.6-\sqrt{122.76}}{18}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12.6)+\sqrt{122.76}}{2*9}=\frac{12.6+\sqrt{122.76}}{18}
$