77/6x+181/2=7/2x+28

Solution for 77/6x+181/2=7/2x+28 equation:

77/6x+181/2=7/2x+28

We move all terms to the left:

77/6x+181/2-(7/2x+28)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 2x+28)!=0

x∈R


We get rid of parentheses

77/6x-7/2x-28+181/2=0

We calculate fractions


616x/48x^2+(-42x)/48x^2+1086x/48x^2-28=0

We multiply all the terms by the denominator


616x+(-42x)+1086x-28*48x^2=0

We add all the numbers together, and all the variables

1702x+(-42x)-28*48x^2=0

Wy multiply elements

-1344x^2+1702x+(-42x)=0

We get rid of parentheses

-1344x^2+1702x-42x=0

We add all the numbers together, and all the variables

-1344x^2+1660x=0

a = -1344; b = 1660; c = 0;
Δ = b2-4ac
Δ = 16602-4·(-1344)·0
Δ = 2755600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2755600}=1660$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1660)-1660}{2*-1344}=\frac{-3320}{-2688}
=1+79/336
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1660)+1660}{2*-1344}=\frac{0}{-2688}
=0
$