3/2x+3=7+x

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

3/2x+3=7+x

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-2x^2-14x+6x+3=0

We add all the numbers together, and all the variables

-2x^2-8x+3=0

a = -2; b = -8; c = +3;
Δ = b2-4ac
Δ = -82-4·(-2)·3
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{22}}{2*-2}=\frac{8-2\sqrt{22}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{22}}{2*-2}=\frac{8+2\sqrt{22}}{-4}
$