(-1/2)t+9=-27;t

Solution for (-1/2)t+9=-27;t equation:

(-1/2)t+9=-27t

We move all terms to the left:

(-1/2)t+9-(-27t)=0


Domain of the equation: 2)t!=0

t!=0/1

t!=0

t∈R


We multiply parentheses

-1t^2-(-27t)+9=0

We get rid of parentheses

-1t^2+27t+9=0

a = -1; b = 27; c = +9;
Δ = b2-4ac
Δ = 272-4·(-1)·9
Δ = 765
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{765}=\sqrt{9*85}=\sqrt{9}*\sqrt{85}=3\sqrt{85}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{85}}{2*-1}=\frac{-27-3\sqrt{85}}{-2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{85}}{2*-1}=\frac{-27+3\sqrt{85}}{-2}
$