x+3/4x=140

Solution for x+3/4x=140 equation:

x+3/4x=140

We move all terms to the left:

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

Wy multiply elements

4x^2-560x+3=0

a = 4; b = -560; c = +3;
Δ = b2-4ac
Δ = -5602-4·4·3
Δ = 313552
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:

$\sqrt{\Delta}=\sqrt{313552}=\sqrt{16*19597}=\sqrt{16}*\sqrt{19597}=4\sqrt{19597}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-560)-4\sqrt{19597}}{2*4}=\frac{560-4\sqrt{19597}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-560)+4\sqrt{19597}}{2*4}=\frac{560+4\sqrt{19597}}{8}
$