6x/4x=77+2x

Solution for 6x/4x=77+2x equation:

6x/4x=77+2x

We move all terms to the left:

6x/4x-(77+2x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

6x/4x-(2x+77)=0

We get rid of parentheses

6x/4x-2x-77=0

We multiply all the terms by the denominator


6x-2x*4x-77*4x=0

Wy multiply elements

-8x^2+6x-308x=0

We add all the numbers together, and all the variables

-8x^2-302x=0

a = -8; b = -302; c = 0;
Δ = b2-4ac
Δ = -3022-4·(-8)·0
Δ = 91204
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{91204}=302$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-302)-302}{2*-8}=\frac{0}{-16}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-302)+302}{2*-8}=\frac{604}{-16}
=-37+3/4
$