3x/4x+5/8=4x

Solution for 3x/4x+5/8=4x equation:

3x/4x+5/8=4x

We move all terms to the left:

3x/4x+5/8-(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+3x/4x+5/8=0

We calculate fractions


-4x+24x/32x+20x/32x=0

We multiply all the terms by the denominator


-4x*32x+24x+20x=0

We add all the numbers together, and all the variables

44x-4x*32x=0

Wy multiply elements

-128x^2+44x=0

a = -128; b = 44; c = 0;
Δ = b2-4ac
Δ = 442-4·(-128)·0
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-44}{2*-128}=\frac{-88}{-256}
=11/32
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+44}{2*-128}=\frac{0}{-256}
=0
$