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

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

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

We move all terms to the left:

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


Domain of the equation: 4)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses

3x^2-4x+5/8=0

We multiply all the terms by the denominator


3x^2*8-4x*8+5=0

Wy multiply elements

24x^2-32x+5=0

a = 24; b = -32; c = +5;
Δ = b2-4ac
Δ = -322-4·24·5
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{34}}{2*24}=\frac{32-4\sqrt{34}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{34}}{2*24}=\frac{32+4\sqrt{34}}{48}
$