t-5=17/t=12

Solution for t-5=17/t=12 equation:

t-5=17/t=12

We move all terms to the left:

t-5-(17/t)=0


Domain of the equation: t)!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

t-(+17/t)-5=0

We get rid of parentheses

t-17/t-5=0

We multiply all the terms by the denominator


t*t-5*t-17=0

We add all the numbers together, and all the variables

-5t+t*t-17=0

Wy multiply elements

t^2-5t-17=0

a = 1; b = -5; c = -17;
Δ = b2-4ac
Δ = -52-4·1·(-17)
Δ = 93
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{93}}{2*1}=\frac{5-\sqrt{93}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{93}}{2*1}=\frac{5+\sqrt{93}}{2}
$