63/4x+7=x

Solution for 63/4x+7=x equation:

63/4x+7=x

We move all terms to the left:

63/4x+7-(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+63/4x+7=0

We multiply all the terms by the denominator


-1x*4x+7*4x+63=0

Wy multiply elements

-4x^2+28x+63=0

a = -4; b = 28; c = +63;
Δ = b2-4ac
Δ = 282-4·(-4)·63
Δ = 1792
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:

$\sqrt{\Delta}=\sqrt{1792}=\sqrt{256*7}=\sqrt{256}*\sqrt{7}=16\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-16\sqrt{7}}{2*-4}=\frac{-28-16\sqrt{7}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+16\sqrt{7}}{2*-4}=\frac{-28+16\sqrt{7}}{-8}
$