h-5/3h=3

Solution for h-5/3h=3 equation:

h-5/3h=3

We move all terms to the left:

h-5/3h-(3)=0


Domain of the equation: 3h!=0

h!=0/3

h!=0

h∈R


We multiply all the terms by the denominator


h*3h-3*3h-5=0

Wy multiply elements

3h^2-9h-5=0

a = 3; b = -9; c = -5;
Δ = b2-4ac
Δ = -92-4·3·(-5)
Δ = 141
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{141}}{2*3}=\frac{9-\sqrt{141}}{6}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{141}}{2*3}=\frac{9+\sqrt{141}}{6}
$