.5x+2/3x=7

Solution for .5x+2/3x=7 equation:

.5x+2/3x=7

We move all terms to the left:

.5x+2/3x-(7)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


(.5x)*3x-7*3x+2=0

We add all the numbers together, and all the variables

(+.5x)*3x-7*3x+2=0

We multiply parentheses

3x^2-7*3x+2=0

Wy multiply elements

3x^2-21x+2=0

a = 3; b = -21; c = +2;
Δ = b2-4ac
Δ = -212-4·3·2
Δ = 417
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{-(-21)-\sqrt{417}}{2*3}=\frac{21-\sqrt{417}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{417}}{2*3}=\frac{21+\sqrt{417}}{6}
$