(7/4)-(8/(12x-8))=x

Solution for (7/4)-(8/(12x-8))=x equation:

(7/4)-(8/(12x-8))=x

We move all terms to the left:

(7/4)-(8/(12x-8))-(x)=0


Domain of the equation: (12x-8))!=0

x∈R


We add all the numbers together, and all the variables

-(8/(12x-8))-x+(+7/4)=0

We add all the numbers together, and all the variables

-1x-(8/(12x-8))+(+7/4)=0

We get rid of parentheses

-1x-(8/(12x-8))+7/4=0

We calculate fractions


-1x+()/48x+84x/48x=0

We multiply all the terms by the denominator


-1x*48x+84x+()=0

We add all the numbers together, and all the variables

84x-1x*48x=0

Wy multiply elements

-48x^2+84x=0

a = -48; b = 84; c = 0;
Δ = b2-4ac
Δ = 842-4·(-48)·0
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-84}{2*-48}=\frac{-168}{-96}
=1+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+84}{2*-48}=\frac{0}{-96}
=0
$