(3+1/2)-(1+1/3)*x=1

Solution for (3+1/2)-(1+1/3)*x=1 equation:

(3+1/2)-(1+1/3)*x=1

We move all terms to the left:

(3+1/2)-(1+1/3)*x-(1)=0


Domain of the equation: 3)*x!=0

x!=0/1

x!=0

x∈R


determiningTheFunctionDomain
-(1+1/3)*x-1+(3+1/2)=0

We add all the numbers together, and all the variables

-(1/3+1)*x-1+(1/2+3)=0

We multiply parentheses

-x^2-x-1+(1/2+3)=0

We get rid of parentheses

-x^2-x-1+3+1/2=0

We multiply all the terms by the denominator


-x^2*2-x*2+1-1*2+3*2=0

We add all the numbers together, and all the variables

-x^2*2-x*2+5=0

Wy multiply elements

-2x^2-2x+5=0

a = -2; b = -2; c = +5;
Δ = b2-4ac
Δ = -22-4·(-2)·5
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{11}}{2*-2}=\frac{2-2\sqrt{11}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{11}}{2*-2}=\frac{2+2\sqrt{11}}{-4}
$