2/h-7=12/h-2h+3

Solution for 2/h-7=12/h-2h+3 equation:

2/h-7=12/h-2h+3

We move all terms to the left:

2/h-7-(12/h-2h+3)=0


Domain of the equation: h!=0

h∈R



Domain of the equation: h-2h+3)!=0

h∈R


We add all the numbers together, and all the variables

2/h-(-2h+12/h+3)-7=0

We get rid of parentheses

2/h+2h-12/h-3-7=0

We multiply all the terms by the denominator


2h*h-3*h-7*h+2-12=0

We add all the numbers together, and all the variables

-10h+2h*h-10=0

Wy multiply elements

2h^2-10h-10=0

a = 2; b = -10; c = -10;
Δ = b2-4ac
Δ = -102-4·2·(-10)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6\sqrt{5}}{2*2}=\frac{10-6\sqrt{5}}{4}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6\sqrt{5}}{2*2}=\frac{10+6\sqrt{5}}{4}
$