3x+14/2x+13+10=6

Solution for 3x+14/2x+13+10=6 equation:

3x+14/2x+13+10=6

We move all terms to the left:

3x+14/2x+13+10-(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

3x+14/2x+17=0

We multiply all the terms by the denominator


3x*2x+17*2x+14=0

Wy multiply elements

6x^2+34x+14=0

a = 6; b = 34; c = +14;
Δ = b2-4ac
Δ = 342-4·6·14
Δ = 820
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:

$\sqrt{\Delta}=\sqrt{820}=\sqrt{4*205}=\sqrt{4}*\sqrt{205}=2\sqrt{205}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{205}}{2*6}=\frac{-34-2\sqrt{205}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{205}}{2*6}=\frac{-34+2\sqrt{205}}{12}
$