H=8t+10t*t

Solution for H=8t+10t*t equation:

=8H+10H*H

We move all terms to the left:

-(8H+10H*H)=0

We add all the numbers together, and all the variables

-(+8H+10H*H)=0

We get rid of parentheses

-8H-10H*H=0

Wy multiply elements

-10H^2-8H=0

a = -10; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-10)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*-10}=\frac{0}{-20}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-10}=\frac{16}{-20}
=-4/5
$