2/3t-5/11t=14

Solution for 2/3t-5/11t=14 equation:

2/3t-5/11t=14

We move all terms to the left:

2/3t-5/11t-(14)=0


Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R



Domain of the equation: 11t!=0

t!=0/11

t!=0

t∈R


We calculate fractions


22t/33t^2+(-15t)/33t^2-14=0

We multiply all the terms by the denominator


22t+(-15t)-14*33t^2=0

Wy multiply elements

-462t^2+22t+(-15t)=0

We get rid of parentheses

-462t^2+22t-15t=0

We add all the numbers together, and all the variables

-462t^2+7t=0

a = -462; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-462)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-462}=\frac{-14}{-924}
=1/66
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-462}=\frac{0}{-924}
=0
$