(2/3)x+(x/2)=7

Solution for (2/3)x+(x/2)=7 equation:

(2/3)x+(x/2)=7

We move all terms to the left:

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


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

2x^2+(+x/2)-7=0

We get rid of parentheses

2x^2+x/2-7=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

2x^2*2+x-14=0

Wy multiply elements

4x^2+x-14=0

a = 4; b = 1; c = -14;
Δ = b2-4ac
Δ = 12-4·4·(-14)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-15}{2*4}=\frac{-16}{8}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+15}{2*4}=\frac{14}{8}
=1+3/4
$