5t+6=3(14/3t-2)

Solution for 5t+6=3(14/3t-2) equation:

5t+6=3(14/3t-2)

We move all terms to the left:

5t+6-(3(14/3t-2))=0


Domain of the equation: 3t-2))!=0

t∈R


We multiply all the terms by the denominator


5t*3t+6*3t-2))-(3(14-2))=0

We add all the numbers together, and all the variables

5t*3t+6*3t-2))-(312)=0

We add all the numbers together, and all the variables

5t*3t+6*3t=0

Wy multiply elements

15t^2+18t=0

a = 15; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·15·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*15}=\frac{-36}{30}
=-1+1/5
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*15}=\frac{0}{30}
=0
$