3x+7/2x+3=16

Solution for 3x+7/2x+3=16 equation:

3x+7/2x+3=16

We move all terms to the left:

3x+7/2x+3-(16)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3x+7/2x-13=0

We multiply all the terms by the denominator


3x*2x-13*2x+7=0

Wy multiply elements

6x^2-26x+7=0

a = 6; b = -26; c = +7;
Δ = b2-4ac
Δ = -262-4·6·7
Δ = 508
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:

$\sqrt{\Delta}=\sqrt{508}=\sqrt{4*127}=\sqrt{4}*\sqrt{127}=2\sqrt{127}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{127}}{2*6}=\frac{26-2\sqrt{127}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{127}}{2*6}=\frac{26+2\sqrt{127}}{12}
$