-3/4h=-h-3

Solution for -3/4h=-h-3 equation:

-3/4h=-h-3

We move all terms to the left:

-3/4h-(-h-3)=0


Domain of the equation: 4h!=0

h!=0/4

h!=0

h∈R


We add all the numbers together, and all the variables

-3/4h-(-1h-3)=0

We get rid of parentheses

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

We multiply all the terms by the denominator


1h*4h+3*4h-3=0

Wy multiply elements

4h^2+12h-3=0

a = 4; b = 12; c = -3;
Δ = b2-4ac
Δ = 122-4·4·(-3)
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-8\sqrt{3}}{2*4}=\frac{-12-8\sqrt{3}}{8}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+8\sqrt{3}}{2*4}=\frac{-12+8\sqrt{3}}{8}
$