5-7t=-3/t

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

5-7t=-3/t

We move all terms to the left:

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


Domain of the equation: t)!=0

t!=0/1

t!=0

t∈R


We get rid of parentheses

-7t+3/t+5=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

5t-7t*t+3=0

Wy multiply elements

-7t^2+5t+3=0

a = -7; b = 5; c = +3;
Δ = b2-4ac
Δ = 52-4·(-7)·3
Δ = 109
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{109}}{2*-7}=\frac{-5-\sqrt{109}}{-14}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{109}}{2*-7}=\frac{-5+\sqrt{109}}{-14}
$