8/t+3=7/9t+5

Solution for 8/t+3=7/9t+5 equation:

8/t+3=7/9t+5

We move all terms to the left:

8/t+3-(7/9t+5)=0


Domain of the equation: t!=0

t∈R



Domain of the equation: 9t+5)!=0

t∈R


We get rid of parentheses

8/t-7/9t-5+3=0

We calculate fractions


72t/9t^2+(-7t)/9t^2-5+3=0

We add all the numbers together, and all the variables

72t/9t^2+(-7t)/9t^2-2=0

We multiply all the terms by the denominator


72t+(-7t)-2*9t^2=0

Wy multiply elements

-18t^2+72t+(-7t)=0

We get rid of parentheses

-18t^2+72t-7t=0

We add all the numbers together, and all the variables

-18t^2+65t=0

a = -18; b = 65; c = 0;
Δ = b2-4ac
Δ = 652-4·(-18)·0
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(65)-65}{2*-18}=\frac{-130}{-36}
=3+11/18
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+65}{2*-18}=\frac{0}{-36}
=0
$