3+13/2h=2+7h

Solution for 3+13/2h=2+7h equation:

3+13/2h=2+7h

We move all terms to the left:

3+13/2h-(2+7h)=0


Domain of the equation: 2h!=0

h!=0/2

h!=0

h∈R


We add all the numbers together, and all the variables

13/2h-(7h+2)+3=0

We get rid of parentheses

13/2h-7h-2+3=0

We multiply all the terms by the denominator


-7h*2h-2*2h+3*2h+13=0

Wy multiply elements

-14h^2-4h+6h+13=0

We add all the numbers together, and all the variables

-14h^2+2h+13=0

a = -14; b = 2; c = +13;
Δ = b2-4ac
Δ = 22-4·(-14)·13
Δ = 732
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:

$\sqrt{\Delta}=\sqrt{732}=\sqrt{4*183}=\sqrt{4}*\sqrt{183}=2\sqrt{183}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{183}}{2*-14}=\frac{-2-2\sqrt{183}}{-28}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{183}}{2*-14}=\frac{-2+2\sqrt{183}}{-28}
$