x-1/4x=140

Solution for x-1/4x=140 equation:

x-1/4x=140

We move all terms to the left:

x-1/4x-(140)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


x*4x-140*4x-1=0

Wy multiply elements

4x^2-560x-1=0

a = 4; b = -560; c = -1;
Δ = b2-4ac
Δ = -5602-4·4·(-1)
Δ = 313616
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:

$\sqrt{\Delta}=\sqrt{313616}=\sqrt{16*19601}=\sqrt{16}*\sqrt{19601}=4\sqrt{19601}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-560)-4\sqrt{19601}}{2*4}=\frac{560-4\sqrt{19601}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-560)+4\sqrt{19601}}{2*4}=\frac{560+4\sqrt{19601}}{8}
$