2/3h+5-h=-3

Solution for 2/3h+5-h=-3 equation:

2/3h+5-h=-3

We move all terms to the left:

2/3h+5-h-(-3)=0


Domain of the equation: 3h!=0

h!=0/3

h!=0

h∈R


We add all the numbers together, and all the variables

-1h+2/3h+8=0

We multiply all the terms by the denominator


-1h*3h+8*3h+2=0

Wy multiply elements

-3h^2+24h+2=0

a = -3; b = 24; c = +2;
Δ = b2-4ac
Δ = 242-4·(-3)·2
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-10\sqrt{6}}{2*-3}=\frac{-24-10\sqrt{6}}{-6}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+10\sqrt{6}}{2*-3}=\frac{-24+10\sqrt{6}}{-6}
$