2/5.h-7=12/5.h-2h+3

Solution for 2/5.h-7=12/5.h-2h+3 equation:

2/5.h-7=12/5.h-2h+3

We move all terms to the left:

2/5.h-7-(12/5.h-2h+3)=0


Domain of the equation: 5.h!=0

h!=0/5.

h!=0

h∈R



Domain of the equation: 5.h-2h+3)!=0

h∈R


We add all the numbers together, and all the variables

2/5.h-(-2h+12/5.h+3)-7=0

We get rid of parentheses

2/5.h+2h-12/5.h-3-7=0

We multiply all the terms by the denominator


2h*5.h-3*5.h-7*5.h+2-12=0

We add all the numbers together, and all the variables

2h*5.h-3*5.h-7*5.h-10=0

Wy multiply elements

10h^2-15h-35h-10=0

We add all the numbers together, and all the variables

10h^2-50h-10=0

a = 10; b = -50; c = -10;
Δ = b2-4ac
Δ = -502-4·10·(-10)
Δ = 2900
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:

$\sqrt{\Delta}=\sqrt{2900}=\sqrt{100*29}=\sqrt{100}*\sqrt{29}=10\sqrt{29}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-10\sqrt{29}}{2*10}=\frac{50-10\sqrt{29}}{20}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+10\sqrt{29}}{2*10}=\frac{50+10\sqrt{29}}{20}
$