2x+7/3x+8=14

Solution for 2x+7/3x+8=14 equation:

2x+7/3x+8=14

We move all terms to the left:

2x+7/3x+8-(14)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2x+7/3x-6=0

We multiply all the terms by the denominator


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

Wy multiply elements

6x^2-18x+7=0

a = 6; b = -18; c = +7;
Δ = b2-4ac
Δ = -182-4·6·7
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{39}}{2*6}=\frac{18-2\sqrt{39}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{39}}{2*6}=\frac{18+2\sqrt{39}}{12}
$