3/4x+5/4x=4x

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

3/4x+5/4x=4x

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-4x+3/4x+5/4x=0

We multiply all the terms by the denominator


-4x*4x+3+5=0

We add all the numbers together, and all the variables

-4x*4x+8=0

Wy multiply elements

-16x^2+8=0

a = -16; b = 0; c = +8;
Δ = b2-4ac
Δ = 02-4·(-16)·8
Δ = 512
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:

$\sqrt{\Delta}=\sqrt{512}=\sqrt{256*2}=\sqrt{256}*\sqrt{2}=16\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{2}}{2*-16}=\frac{0-16\sqrt{2}}{-32}
=-\frac{16\sqrt{2}}{-32}
=-\frac{\sqrt{2}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{2}}{2*-16}=\frac{0+16\sqrt{2}}{-32}
=\frac{16\sqrt{2}}{-32}
=\frac{\sqrt{2}}{-2}
$