6x-4=1/4x-88

Solution for 6x-4=1/4x-88 equation:

6x-4=1/4x-88

We move all terms to the left:

6x-4-(1/4x-88)=0


Domain of the equation: 4x-88)!=0

x∈R


We get rid of parentheses

6x-1/4x+88-4=0

We multiply all the terms by the denominator


6x*4x+88*4x-4*4x-1=0

Wy multiply elements

24x^2+352x-16x-1=0

We add all the numbers together, and all the variables

24x^2+336x-1=0

a = 24; b = 336; c = -1;
Δ = b2-4ac
Δ = 3362-4·24·(-1)
Δ = 112992
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:

$\sqrt{\Delta}=\sqrt{112992}=\sqrt{16*7062}=\sqrt{16}*\sqrt{7062}=4\sqrt{7062}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(336)-4\sqrt{7062}}{2*24}=\frac{-336-4\sqrt{7062}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(336)+4\sqrt{7062}}{2*24}=\frac{-336+4\sqrt{7062}}{48}
$