1/4x=x+44

Solution for 1/4x=x+44 equation:

1/4x=x+44

We move all terms to the left:

1/4x-(x+44)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x-x-44=0

We multiply all the terms by the denominator


-x*4x-44*4x+1=0

Wy multiply elements

-4x^2-176x+1=0

a = -4; b = -176; c = +1;
Δ = b2-4ac
Δ = -1762-4·(-4)·1
Δ = 30992
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:

$\sqrt{\Delta}=\sqrt{30992}=\sqrt{16*1937}=\sqrt{16}*\sqrt{1937}=4\sqrt{1937}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-176)-4\sqrt{1937}}{2*-4}=\frac{176-4\sqrt{1937}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-176)+4\sqrt{1937}}{2*-4}=\frac{176+4\sqrt{1937}}{-8}
$