1/4h+5=-h-15

Solution for 1/4h+5=-h-15 equation:

1/4h+5=-h-15

We move all terms to the left:

1/4h+5-(-h-15)=0


Domain of the equation: 4h!=0

h!=0/4

h!=0

h∈R


We add all the numbers together, and all the variables

1/4h-(-1h-15)+5=0

We get rid of parentheses

1/4h+1h+15+5=0

We multiply all the terms by the denominator


1h*4h+15*4h+5*4h+1=0

Wy multiply elements

4h^2+60h+20h+1=0

We add all the numbers together, and all the variables

4h^2+80h+1=0

a = 4; b = 80; c = +1;
Δ = b2-4ac
Δ = 802-4·4·1
Δ = 6384
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:

$\sqrt{\Delta}=\sqrt{6384}=\sqrt{16*399}=\sqrt{16}*\sqrt{399}=4\sqrt{399}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-4\sqrt{399}}{2*4}=\frac{-80-4\sqrt{399}}{8}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+4\sqrt{399}}{2*4}=\frac{-80+4\sqrt{399}}{8}
$