T=6000+2b^2/b

Solution for T=6000+2b^2/b equation:

=6000+2T^2/T

We move all terms to the left:

-(6000+2T^2/T)=0


Domain of the equation: T)!=0

T!=0/1

T!=0

T∈R


We get rid of parentheses

-2T^2/T-6000=0

We multiply all the terms by the denominator


-2T^2-6000*T=0

We add all the numbers together, and all the variables

-2T^2-6000T=0

a = -2; b = -6000; c = 0;
Δ = b2-4ac
Δ = -60002-4·(-2)·0
Δ = 36000000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$T_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$T_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36000000}=6000$
$T_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6000)-6000}{2*-2}=\frac{0}{-4}
=0
$
$T_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6000)+6000}{2*-2}=\frac{12000}{-4}
=-3000
$