3+3/2x+4=9x+6

Solution for 3+3/2x+4=9x+6 equation:

3+3/2x+4=9x+6

We move all terms to the left:

3+3/2x+4-(9x+6)=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-(9x+6)+7=0

We get rid of parentheses

3/2x-9x-6+7=0

We multiply all the terms by the denominator


-9x*2x-6*2x+7*2x+3=0

Wy multiply elements

-18x^2-12x+14x+3=0

We add all the numbers together, and all the variables

-18x^2+2x+3=0

a = -18; b = 2; c = +3;
Δ = b2-4ac
Δ = 22-4·(-18)·3
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{55}}{2*-18}=\frac{-2-2\sqrt{55}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{55}}{2*-18}=\frac{-2+2\sqrt{55}}{-36}
$