1=4x-1/6x+7

Solution for 1=4x-1/6x+7 equation:

1=4x-1/6x+7

We move all terms to the left:

1-(4x-1/6x+7)=0


Domain of the equation: 6x+7)!=0

x∈R


We get rid of parentheses

-4x+1/6x-7+1=0

We multiply all the terms by the denominator


-4x*6x-7*6x+1*6x+1=0

Wy multiply elements

-24x^2-42x+6x+1=0

We add all the numbers together, and all the variables

-24x^2-36x+1=0

a = -24; b = -36; c = +1;
Δ = b2-4ac
Δ = -362-4·(-24)·1
Δ = 1392
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:

$\sqrt{\Delta}=\sqrt{1392}=\sqrt{16*87}=\sqrt{16}*\sqrt{87}=4\sqrt{87}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{87}}{2*-24}=\frac{36-4\sqrt{87}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{87}}{2*-24}=\frac{36+4\sqrt{87}}{-48}
$