3/4x-14=x

Solution for 3/4x-14=x equation:

3/4x-14=x

We move all terms to the left:

3/4x-14-(x)=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+3/4x-14=0

We multiply all the terms by the denominator


-1x*4x-14*4x+3=0

Wy multiply elements

-4x^2-56x+3=0

a = -4; b = -56; c = +3;
Δ = b2-4ac
Δ = -562-4·(-4)·3
Δ = 3184
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:

$\sqrt{\Delta}=\sqrt{3184}=\sqrt{16*199}=\sqrt{16}*\sqrt{199}=4\sqrt{199}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-4\sqrt{199}}{2*-4}=\frac{56-4\sqrt{199}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+4\sqrt{199}}{2*-4}=\frac{56+4\sqrt{199}}{-8}
$