-5h-3h+4-2/3h-16h-24-4h+6=-24+h

Solution for -5h-3h+4-2/3h-16h-24-4h+6=-24+h equation:

-5h-3h+4-2/3h-16h-24-4h+6=-24+h

We move all terms to the left:

-5h-3h+4-2/3h-16h-24-4h+6-(-24+h)=0


Domain of the equation: 3h!=0

h!=0/3

h!=0

h∈R


We add all the numbers together, and all the variables

-5h-3h-2/3h-16h-4h-(h-24)+4-24+6=0

We add all the numbers together, and all the variables

-28h-2/3h-(h-24)-14=0

We get rid of parentheses

-28h-2/3h-h+24-14=0

We multiply all the terms by the denominator


-28h*3h-h*3h+24*3h-14*3h-2=0

Wy multiply elements

-84h^2-3h^2+72h-42h-2=0

We add all the numbers together, and all the variables

-87h^2+30h-2=0

a = -87; b = 30; c = -2;
Δ = b2-4ac
Δ = 302-4·(-87)·(-2)
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{51}}{2*-87}=\frac{-30-2\sqrt{51}}{-174}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{51}}{2*-87}=\frac{-30+2\sqrt{51}}{-174}
$