14/4x+5=7/4x+6x

Solution for 14/4x+5=7/4x+6x equation:

14/4x+5=7/4x+6x

We move all terms to the left:

14/4x+5-(7/4x+6x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 4x+6x)!=0

x∈R


We add all the numbers together, and all the variables

14/4x-(+6x+7/4x)+5=0

We get rid of parentheses

14/4x-6x-7/4x+5=0

We multiply all the terms by the denominator


-6x*4x+5*4x+14-7=0

We add all the numbers together, and all the variables

-6x*4x+5*4x+7=0

Wy multiply elements

-24x^2+20x+7=0

a = -24; b = 20; c = +7;
Δ = b2-4ac
Δ = 202-4·(-24)·7
Δ = 1072
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:

$\sqrt{\Delta}=\sqrt{1072}=\sqrt{16*67}=\sqrt{16}*\sqrt{67}=4\sqrt{67}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{67}}{2*-24}=\frac{-20-4\sqrt{67}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{67}}{2*-24}=\frac{-20+4\sqrt{67}}{-48}
$