1/4h+2=2/5h-1

Solution for 1/4h+2=2/5h-1 equation:

1/4h+2=2/5h-1

We move all terms to the left:

1/4h+2-(2/5h-1)=0


Domain of the equation: 4h!=0

h!=0/4

h!=0

h∈R



Domain of the equation: 5h-1)!=0

h∈R


We get rid of parentheses

1/4h-2/5h+1+2=0

We calculate fractions


5h/20h^2+(-8h)/20h^2+1+2=0

We add all the numbers together, and all the variables

5h/20h^2+(-8h)/20h^2+3=0

We multiply all the terms by the denominator


5h+(-8h)+3*20h^2=0

Wy multiply elements

60h^2+5h+(-8h)=0

We get rid of parentheses

60h^2+5h-8h=0

We add all the numbers together, and all the variables

60h^2-3h=0

a = 60; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·60·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*60}=\frac{0}{120}
=0
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*60}=\frac{6}{120}
=1/20
$