7/2x+7=9+3x

Solution for 7/2x+7=9+3x equation:

7/2x+7=9+3x

We move all terms to the left:

7/2x+7-(9+3x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

7/2x-(3x+9)+7=0

We get rid of parentheses

7/2x-3x-9+7=0

We multiply all the terms by the denominator


-3x*2x-9*2x+7*2x+7=0

Wy multiply elements

-6x^2-18x+14x+7=0

We add all the numbers together, and all the variables

-6x^2-4x+7=0

a = -6; b = -4; c = +7;
Δ = b2-4ac
Δ = -42-4·(-6)·7
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{46}}{2*-6}=\frac{4-2\sqrt{46}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{46}}{2*-6}=\frac{4+2\sqrt{46}}{-12}
$