3/4x+2x+1=4x-3

Solution for 3/4x+2x+1=4x-3 equation:

3/4x+2x+1=4x-3

We move all terms to the left:

3/4x+2x+1-(4x-3)=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+3/4x-(4x-3)+1=0

We get rid of parentheses

2x+3/4x-4x+3+1=0

We multiply all the terms by the denominator


2x*4x-4x*4x+3*4x+1*4x+3=0

Wy multiply elements

8x^2-16x^2+12x+4x+3=0

We add all the numbers together, and all the variables

-8x^2+16x+3=0

a = -8; b = 16; c = +3;
Δ = b2-4ac
Δ = 162-4·(-8)·3
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{22}}{2*-8}=\frac{-16-4\sqrt{22}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{22}}{2*-8}=\frac{-16+4\sqrt{22}}{-16}
$