21/3x+10+52/3x-91/2x=121/2

Solution for 21/3x+10+52/3x-91/2x=121/2 equation:

21/3x+10+52/3x-91/2x=121/2

We move all terms to the left:

21/3x+10+52/3x-91/2x-(121/2)=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

21/3x+52/3x-91/2x+10-(+121/2)=0

We get rid of parentheses

21/3x+52/3x-91/2x+10-121/2=0

We calculate fractions


(416x+21)/24x^2+(-273x)/24x^2+(-363x)/24x^2+10=0

We multiply all the terms by the denominator


(416x+21)+(-273x)+(-363x)+10*24x^2=0

Wy multiply elements

240x^2+(416x+21)+(-273x)+(-363x)=0

We get rid of parentheses

240x^2+416x-273x-363x+21=0

We add all the numbers together, and all the variables

240x^2-220x+21=0

a = 240; b = -220; c = +21;
Δ = b2-4ac
Δ = -2202-4·240·21
Δ = 28240
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{28240}=\sqrt{16*1765}=\sqrt{16}*\sqrt{1765}=4\sqrt{1765}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-220)-4\sqrt{1765}}{2*240}=\frac{220-4\sqrt{1765}}{480}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-220)+4\sqrt{1765}}{2*240}=\frac{220+4\sqrt{1765}}{480}
$