3/4x+3=5x-2-3x

Solution for 3/4x+3=5x-2-3x equation:

3/4x+3=5x-2-3x

We move all terms to the left:

3/4x+3-(5x-2-3x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-8x^2+20x+3=0

a = -8; b = 20; c = +3;
Δ = b2-4ac
Δ = 202-4·(-8)·3
Δ = 496
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:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{31}}{2*-8}=\frac{-20-4\sqrt{31}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{31}}{2*-8}=\frac{-20+4\sqrt{31}}{-16}
$