1/4x=x-21

Solution for 1/4x=x-21 equation:

1/4x=x-21

We move all terms to the left:

1/4x-(x-21)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x-x+21=0

We multiply all the terms by the denominator


-x*4x+21*4x+1=0

Wy multiply elements

-4x^2+84x+1=0

a = -4; b = 84; c = +1;
Δ = b2-4ac
Δ = 842-4·(-4)·1
Δ = 7072
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:

$\sqrt{\Delta}=\sqrt{7072}=\sqrt{16*442}=\sqrt{16}*\sqrt{442}=4\sqrt{442}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-4\sqrt{442}}{2*-4}=\frac{-84-4\sqrt{442}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+4\sqrt{442}}{2*-4}=\frac{-84+4\sqrt{442}}{-8}
$