3t-7=5t/6t

Solution for 3t-7=5t/6t equation:

3t-7=5t/6t

We move all terms to the left:

3t-7-(5t/6t)=0


Domain of the equation: 6t)!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

3t-(+5t/6t)-7=0

We get rid of parentheses

3t-5t/6t-7=0

We multiply all the terms by the denominator


3t*6t-5t-7*6t=0

We add all the numbers together, and all the variables

-5t+3t*6t-7*6t=0

Wy multiply elements

18t^2-5t-42t=0

We add all the numbers together, and all the variables

18t^2-47t=0

a = 18; b = -47; c = 0;
Δ = b2-4ac
Δ = -472-4·18·0
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-47}{2*18}=\frac{0}{36}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+47}{2*18}=\frac{94}{36}
=2+11/18
$