2/5h-1/3h+11=8

Solution for 2/5h-1/3h+11=8 equation:

2/5h-1/3h+11=8

We move all terms to the left:

2/5h-1/3h+11-(8)=0


Domain of the equation: 5h!=0

h!=0/5

h!=0

h∈R



Domain of the equation: 3h!=0

h!=0/3

h!=0

h∈R


We add all the numbers together, and all the variables

2/5h-1/3h+3=0

We calculate fractions


6h/15h^2+(-5h)/15h^2+3=0

We multiply all the terms by the denominator


6h+(-5h)+3*15h^2=0

Wy multiply elements

45h^2+6h+(-5h)=0

We get rid of parentheses

45h^2+6h-5h=0

We add all the numbers together, and all the variables

45h^2+h=0

a = 45; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·45·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*45}=\frac{-2}{90}
=-1/45
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*45}=\frac{0}{90}
=0
$