-2/3x-16-7/2x=-116

Solution for -2/3x-16-7/2x=-116 equation:

-2/3x-16-7/2x=-116

We move all terms to the left:

-2/3x-16-7/2x-(-116)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-2/3x-7/2x+100=0

We calculate fractions


(-4x)/6x^2+(-21x)/6x^2+100=0

We multiply all the terms by the denominator


(-4x)+(-21x)+100*6x^2=0

Wy multiply elements

600x^2+(-4x)+(-21x)=0

We get rid of parentheses

600x^2-4x-21x=0

We add all the numbers together, and all the variables

600x^2-25x=0

a = 600; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·600·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-25}{2*600}=\frac{0}{1200}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*600}=\frac{50}{1200}
=1/24
$