t=3/5t+108

Solution for t=3/5t+108 equation:

t=3/5t+108

We move all terms to the left:

t-(3/5t+108)=0


Domain of the equation: 5t+108)!=0

t∈R


We get rid of parentheses

t-3/5t-108=0

We multiply all the terms by the denominator


t*5t-108*5t-3=0

Wy multiply elements

5t^2-540t-3=0

a = 5; b = -540; c = -3;
Δ = b2-4ac
Δ = -5402-4·5·(-3)
Δ = 291660
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:

$\sqrt{\Delta}=\sqrt{291660}=\sqrt{4*72915}=\sqrt{4}*\sqrt{72915}=2\sqrt{72915}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-540)-2\sqrt{72915}}{2*5}=\frac{540-2\sqrt{72915}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-540)+2\sqrt{72915}}{2*5}=\frac{540+2\sqrt{72915}}{10}
$