2t+6/t+9=2

Solution for 2t+6/t+9=2 equation:

2t+6/t+9=2

We move all terms to the left:

2t+6/t+9-(2)=0


Domain of the equation: t!=0

t∈R


We add all the numbers together, and all the variables

2t+6/t+7=0

We multiply all the terms by the denominator


2t*t+7*t+6=0

We add all the numbers together, and all the variables

7t+2t*t+6=0

Wy multiply elements

2t^2+7t+6=0

a = 2; b = 7; c = +6;
Δ = b2-4ac
Δ = 72-4·2·6
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-1}{2*2}=\frac{-8}{4}
=-2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+1}{2*2}=\frac{-6}{4}
=-1+1/2
$