H(t)=30/11t-24

Solution for H(t)=30/11t-24 equation:

(H)=30/11H-24

We move all terms to the left:

(H)-(30/11H-24)=0


Domain of the equation: 11H-24)!=0

H∈R


We get rid of parentheses

H-30/11H+24=0

We multiply all the terms by the denominator


H*11H+24*11H-30=0

Wy multiply elements

11H^2+264H-30=0

a = 11; b = 264; c = -30;
Δ = b2-4ac
Δ = 2642-4·11·(-30)
Δ = 71016
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{71016}=\sqrt{4*17754}=\sqrt{4}*\sqrt{17754}=2\sqrt{17754}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(264)-2\sqrt{17754}}{2*11}=\frac{-264-2\sqrt{17754}}{22}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(264)+2\sqrt{17754}}{2*11}=\frac{-264+2\sqrt{17754}}{22}
$