t-8/t=9

Solution for t-8/t=9 equation:

t-8/t=9

We move all terms to the left:

t-8/t-(9)=0


Domain of the equation: t!=0

t∈R


We multiply all the terms by the denominator


t*t-9*t-8=0

We add all the numbers together, and all the variables

-9t+t*t-8=0

Wy multiply elements

t^2-9t-8=0

a = 1; b = -9; c = -8;
Δ = b2-4ac
Δ = -92-4·1·(-8)
Δ = 113
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{-(-9)-\sqrt{113}}{2*1}=\frac{9-\sqrt{113}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{113}}{2*1}=\frac{9+\sqrt{113}}{2}
$