H=5t^2+8t+3

Solution for H=5t^2+8t+3 equation:

=5H^2+8H+3

We move all terms to the left:

-(5H^2+8H+3)=0

We get rid of parentheses

-5H^2-8H-3=0

a = -5; b = -8; c = -3;
Δ = b2-4ac
Δ = -82-4·(-5)·(-3)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2}{2*-5}=\frac{6}{-10}
=-3/5
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2}{2*-5}=\frac{10}{-10}
=-1
$