5.6666+1/2x=4.1666+.75x

Solution for 5.6666+1/2x=4.1666+.75x equation:

5.6666+1/2x=4.1666+.75x

We move all terms to the left:

5.6666+1/2x-(4.1666+.75x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(.75x+4.1666)+5.6666=0

We get rid of parentheses

1/2x-.75x-4.1666+5.6666=0

We multiply all the terms by the denominator


-(.75x)*2x-(4.1666)*2x+(5.6666)*2x+1=0

We add all the numbers together, and all the variables

-(+.75x)*2x-(4.1666)*2x+(5.6666)*2x+1=0

We multiply parentheses

-2x^2-8.3332x+11.3332x+1=0

We add all the numbers together, and all the variables

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

a = -2; b = 3; c = +1;
Δ = b2-4ac
Δ = 32-4·(-2)·1
Δ = 17
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{17}}{2*-2}=\frac{-3-\sqrt{17}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{17}}{2*-2}=\frac{-3+\sqrt{17}}{-4}
$