3/4x-2=5x+6

Solution for 3/4x-2=5x+6 equation:

3/4x-2=5x+6

We move all terms to the left:

3/4x-2-(5x+6)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

3/4x-5x-6-2=0

We multiply all the terms by the denominator


-5x*4x-6*4x-2*4x+3=0

Wy multiply elements

-20x^2-24x-8x+3=0

We add all the numbers together, and all the variables

-20x^2-32x+3=0

a = -20; b = -32; c = +3;
Δ = b2-4ac
Δ = -322-4·(-20)·3
Δ = 1264
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:

$\sqrt{\Delta}=\sqrt{1264}=\sqrt{16*79}=\sqrt{16}*\sqrt{79}=4\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{79}}{2*-20}=\frac{32-4\sqrt{79}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{79}}{2*-20}=\frac{32+4\sqrt{79}}{-40}
$