3/5h-10+1/5h=12+1/3h-8

Solution for 3/5h-10+1/5h=12+1/3h-8 equation:

3/5h-10+1/5h=12+1/3h-8

We move all terms to the left:

3/5h-10+1/5h-(12+1/3h-8)=0


Domain of the equation: 5h!=0

h!=0/5

h!=0

h∈R



Domain of the equation: 3h-8)!=0

h∈R


We add all the numbers together, and all the variables

3/5h+1/5h-(1/3h+4)-10=0

We get rid of parentheses

3/5h+1/5h-1/3h-4-10=0

We calculate fractions


(3h+3)/15h^2+(-5h)/15h^2-4-10=0

We add all the numbers together, and all the variables

(3h+3)/15h^2+(-5h)/15h^2-14=0

We multiply all the terms by the denominator


(3h+3)+(-5h)-14*15h^2=0

Wy multiply elements

-210h^2+(3h+3)+(-5h)=0

We get rid of parentheses

-210h^2+3h-5h+3=0

We add all the numbers together, and all the variables

-210h^2-2h+3=0

a = -210; b = -2; c = +3;
Δ = b2-4ac
Δ = -22-4·(-210)·3
Δ = 2524
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:

$\sqrt{\Delta}=\sqrt{2524}=\sqrt{4*631}=\sqrt{4}*\sqrt{631}=2\sqrt{631}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{631}}{2*-210}=\frac{2-2\sqrt{631}}{-420}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{631}}{2*-210}=\frac{2+2\sqrt{631}}{-420}
$