4/3t=5-6/15t

Solution for 4/3t=5-6/15t equation:

4/3t=5-6/15t

We move all terms to the left:

4/3t-(5-6/15t)=0


Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R



Domain of the equation: 15t)!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

4/3t-(-6/15t+5)=0

We get rid of parentheses

4/3t+6/15t-5=0

We calculate fractions


60t/45t^2+18t/45t^2-5=0

We multiply all the terms by the denominator


60t+18t-5*45t^2=0

We add all the numbers together, and all the variables

78t-5*45t^2=0

Wy multiply elements

-225t^2+78t=0

a = -225; b = 78; c = 0;
Δ = b2-4ac
Δ = 782-4·(-225)·0
Δ = 6084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6084}=78$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-78}{2*-225}=\frac{-156}{-450}
=26/75
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+78}{2*-225}=\frac{0}{-450}
=0
$