8/5h=2h+8

Solution for 8/5h=2h+8 equation:

8/5h=2h+8

We move all terms to the left:

8/5h-(2h+8)=0


Domain of the equation: 5h!=0

h!=0/5

h!=0

h∈R


We get rid of parentheses

8/5h-2h-8=0

We multiply all the terms by the denominator


-2h*5h-8*5h+8=0

Wy multiply elements

-10h^2-40h+8=0

a = -10; b = -40; c = +8;
Δ = b2-4ac
Δ = -402-4·(-10)·8
Δ = 1920
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:

$\sqrt{\Delta}=\sqrt{1920}=\sqrt{64*30}=\sqrt{64}*\sqrt{30}=8\sqrt{30}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-8\sqrt{30}}{2*-10}=\frac{40-8\sqrt{30}}{-20}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+8\sqrt{30}}{2*-10}=\frac{40+8\sqrt{30}}{-20}
$