7/4x-x=12

Solution for 7/4x-x=12 equation:

7/4x-x=12

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+7/4x-12=0

We multiply all the terms by the denominator


-1x*4x-12*4x+7=0

Wy multiply elements

-4x^2-48x+7=0

a = -4; b = -48; c = +7;
Δ = b2-4ac
Δ = -482-4·(-4)·7
Δ = 2416
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:

$\sqrt{\Delta}=\sqrt{2416}=\sqrt{16*151}=\sqrt{16}*\sqrt{151}=4\sqrt{151}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{151}}{2*-4}=\frac{48-4\sqrt{151}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{151}}{2*-4}=\frac{48+4\sqrt{151}}{-8}
$