3/4x-4=2x+3

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

3/4x-4=2x+3

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-8x^2-28x+3=0

a = -8; b = -28; c = +3;
Δ = b2-4ac
Δ = -282-4·(-8)·3
Δ = 880
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:

$\sqrt{\Delta}=\sqrt{880}=\sqrt{16*55}=\sqrt{16}*\sqrt{55}=4\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{55}}{2*-8}=\frac{28-4\sqrt{55}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{55}}{2*-8}=\frac{28+4\sqrt{55}}{-16}
$