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

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

2/5h-7=12.5h+3

We move all terms to the left:

2/5h-7-(12.5h+3)=0


Domain of the equation: 5h!=0

h!=0/5

h!=0

h∈R


We get rid of parentheses

2/5h-12.5h-3-7=0

We multiply all the terms by the denominator


-(12.5h)*5h-3*5h-7*5h+2=0

We add all the numbers together, and all the variables

-(+12.5h)*5h-3*5h-7*5h+2=0

We multiply parentheses

-60h^2-3*5h-7*5h+2=0

Wy multiply elements

-60h^2-15h-35h+2=0

We add all the numbers together, and all the variables

-60h^2-50h+2=0

a = -60; b = -50; c = +2;
Δ = b2-4ac
Δ = -502-4·(-60)·2
Δ = 2980
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:

$\sqrt{\Delta}=\sqrt{2980}=\sqrt{4*745}=\sqrt{4}*\sqrt{745}=2\sqrt{745}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{745}}{2*-60}=\frac{50-2\sqrt{745}}{-120}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{745}}{2*-60}=\frac{50+2\sqrt{745}}{-120}
$