t=9.09(t-32.5)t-32.5)+34000

Solution for t=9.09(t-32.5)t-32.5)+34000 equation:

t=9.09(t-32.5)t-32.5)+34000

We move all terms to the left:

t-(9.09(t-32.5)t-32.5)+34000)=0

We add all the numbers together, and all the variables

t-(9.09(t-32.5)t-32.5)=0


We calculate terms in parentheses: -(9.09(t-32.5)t-32.5), so:

9.09(t-32.5)t-32.5

We multiply parentheses

9t^2-292.5t-32.5

Back to the equation:

-(9t^2-292.5t-32.5)


We get rid of parentheses

-9t^2+t+292.5t+32.5=0

We add all the numbers together, and all the variables

-9t^2+293.5t+32.5=0

a = -9; b = 293.5; c = +32.5;
Δ = b2-4ac
Δ = 293.52-4·(-9)·32.5
Δ = 87312.25
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{-(293.5)-\sqrt{87312.25}}{2*-9}=\frac{-293.5-\sqrt{87312.25}}{-18}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(293.5)+\sqrt{87312.25}}{2*-9}=\frac{-293.5+\sqrt{87312.25}}{-18}
$