x-3x+5/4x=20

Solution for x-3x+5/4x=20 equation:

x-3x+5/4x=20

We move all terms to the left:

x-3x+5/4x-(20)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-2x+5/4x-20=0

We multiply all the terms by the denominator


-2x*4x-20*4x+5=0

Wy multiply elements

-8x^2-80x+5=0

a = -8; b = -80; c = +5;
Δ = b2-4ac
Δ = -802-4·(-8)·5
Δ = 6560
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:

$\sqrt{\Delta}=\sqrt{6560}=\sqrt{16*410}=\sqrt{16}*\sqrt{410}=4\sqrt{410}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-4\sqrt{410}}{2*-8}=\frac{80-4\sqrt{410}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+4\sqrt{410}}{2*-8}=\frac{80+4\sqrt{410}}{-16}
$