3h=7(2/7-37h)-10

Solution for 3h=7(2/7-37h)-10 equation:

3h=7(2/7-37h)-10

We move all terms to the left:

3h-(7(2/7-37h)-10)=0


Domain of the equation: 7-37h)-10)!=0

We move all terms containing h to the left, all other terms to the right

-37h)-10)!=-7

h!=-7/1

h!=-7

h∈R


We add all the numbers together, and all the variables

3h-(7(-37h+2/7)-10)=0

We multiply all the terms by the denominator


3h*7)-10)-(7(-37h+2=0

We add all the numbers together, and all the variables

-37h+3h*7)-10)-(7(+2=0

Wy multiply elements

21h^2-37h+2=0

a = 21; b = -37; c = +2;
Δ = b2-4ac
Δ = -372-4·21·2
Δ = 1201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-\sqrt{1201}}{2*21}=\frac{37-\sqrt{1201}}{42}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+\sqrt{1201}}{2*21}=\frac{37+\sqrt{1201}}{42}
$