t/3t-7=4t-7

Solution for t/3t-7=4t-7 equation:

t/3t-7=4t-7

We move all terms to the left:

t/3t-7-(4t-7)=0


Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R


We get rid of parentheses

t/3t-4t+7-7=0

We multiply all the terms by the denominator


t-4t*3t+7*3t-7*3t=0

Wy multiply elements

-12t^2+t+21t-21t=0

We add all the numbers together, and all the variables

-12t^2+t=0

a = -12; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-12)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-12}=\frac{-2}{-24}
=1/12
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-12}=\frac{0}{-24}
=0
$