77/3h=92-2h

Solution for 77/3h=92-2h equation:

77/3h=92-2h

We move all terms to the left:

77/3h-(92-2h)=0


Domain of the equation: 3h!=0

h!=0/3

h!=0

h∈R


We add all the numbers together, and all the variables

77/3h-(-2h+92)=0

We get rid of parentheses

77/3h+2h-92=0

We multiply all the terms by the denominator


2h*3h-92*3h+77=0

Wy multiply elements

6h^2-276h+77=0

a = 6; b = -276; c = +77;
Δ = b2-4ac
Δ = -2762-4·6·77
Δ = 74328
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:

$\sqrt{\Delta}=\sqrt{74328}=\sqrt{4*18582}=\sqrt{4}*\sqrt{18582}=2\sqrt{18582}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-276)-2\sqrt{18582}}{2*6}=\frac{276-2\sqrt{18582}}{12}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-276)+2\sqrt{18582}}{2*6}=\frac{276+2\sqrt{18582}}{12}
$