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

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

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

We move all terms to the left:

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

We get rid of parentheses

3/2x-4x-9+7=0

We multiply all the terms by the denominator


-4x*2x-9*2x+7*2x+3=0

Wy multiply elements

-8x^2-18x+14x+3=0

We add all the numbers together, and all the variables

-8x^2-4x+3=0

a = -8; b = -4; c = +3;
Δ = b2-4ac
Δ = -42-4·(-8)·3
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{7}}{2*-8}=\frac{4-4\sqrt{7}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{7}}{2*-8}=\frac{4+4\sqrt{7}}{-16}
$