H(t)=-1/5t+12

Solution for H(t)=-1/5t+12 equation:

(H)=-1/5H+12

We move all terms to the left:

(H)-(-1/5H+12)=0


Domain of the equation: 5H+12)!=0

H∈R


We get rid of parentheses

H+1/5H-12=0

We multiply all the terms by the denominator


H*5H-12*5H+1=0

Wy multiply elements

5H^2-60H+1=0

a = 5; b = -60; c = +1;
Δ = b2-4ac
Δ = -602-4·5·1
Δ = 3580
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:

$\sqrt{\Delta}=\sqrt{3580}=\sqrt{4*895}=\sqrt{4}*\sqrt{895}=2\sqrt{895}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{895}}{2*5}=\frac{60-2\sqrt{895}}{10}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{895}}{2*5}=\frac{60+2\sqrt{895}}{10}
$