3/4x-6=7x+3

Solution for 3/4x-6=7x+3 equation:

3/4x-6=7x+3

We move all terms to the left:

3/4x-6-(7x+3)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

3/4x-7x-3-6=0

We multiply all the terms by the denominator


-7x*4x-3*4x-6*4x+3=0

Wy multiply elements

-28x^2-12x-24x+3=0

We add all the numbers together, and all the variables

-28x^2-36x+3=0

a = -28; b = -36; c = +3;
Δ = b2-4ac
Δ = -362-4·(-28)·3
Δ = 1632
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:

$\sqrt{\Delta}=\sqrt{1632}=\sqrt{16*102}=\sqrt{16}*\sqrt{102}=4\sqrt{102}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{102}}{2*-28}=\frac{36-4\sqrt{102}}{-56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{102}}{2*-28}=\frac{36+4\sqrt{102}}{-56}
$