5/t-3-30/t*2-9=1

Solution for 5/t-3-30/t*2-9=1 equation:

5/t-3-30/t*2-9=1

We move all terms to the left:

5/t-3-30/t*2-9-(1)=0


Domain of the equation: t!=0

t∈R



Domain of the equation: t*2!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

5/t-30/t*2-13=0

We calculate fractions


20t/4t^2+(-30t)/4t^2-13=0

We multiply all the terms by the denominator


20t+(-30t)-13*4t^2=0

Wy multiply elements

-52t^2+20t+(-30t)=0

We get rid of parentheses

-52t^2+20t-30t=0

We add all the numbers together, and all the variables

-52t^2-10t=0

a = -52; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·(-52)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*-52}=\frac{0}{-104}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*-52}=\frac{20}{-104}
=-5/26
$