2(7+3t)=-2/3t

Solution for 2(7+3t)=-2/3t equation:

2(7+3t)=-2/3t

We move all terms to the left:

2(7+3t)-(-2/3t)=0


Domain of the equation: 3t)!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

2(3t+7)-(-2/3t)=0

We multiply parentheses

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

We get rid of parentheses

6t+2/3t+14=0

We multiply all the terms by the denominator


6t*3t+14*3t+2=0

Wy multiply elements

18t^2+42t+2=0

a = 18; b = 42; c = +2;
Δ = b2-4ac
Δ = 422-4·18·2
Δ = 1620
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1620}=\sqrt{324*5}=\sqrt{324}*\sqrt{5}=18\sqrt{5}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-18\sqrt{5}}{2*18}=\frac{-42-18\sqrt{5}}{36}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+18\sqrt{5}}{2*18}=\frac{-42+18\sqrt{5}}{36}
$