x-3/4x=80

Solution for x-3/4x=80 equation:

x-3/4x=80

We move all terms to the left:

x-3/4x-(80)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


x*4x-80*4x-3=0

Wy multiply elements

4x^2-320x-3=0

a = 4; b = -320; c = -3;
Δ = b2-4ac
Δ = -3202-4·4·(-3)
Δ = 102448
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:

$\sqrt{\Delta}=\sqrt{102448}=\sqrt{16*6403}=\sqrt{16}*\sqrt{6403}=4\sqrt{6403}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-320)-4\sqrt{6403}}{2*4}=\frac{320-4\sqrt{6403}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-320)+4\sqrt{6403}}{2*4}=\frac{320+4\sqrt{6403}}{8}
$