4x/6x-7-8=7/5x

Solution for 4x/6x-7-8=7/5x equation:

4x/6x-7-8=7/5x

We move all terms to the left:

4x/6x-7-8-(7/5x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4x/6x-(+7/5x)-7-8=0

We add all the numbers together, and all the variables

4x/6x-(+7/5x)-15=0

We get rid of parentheses

4x/6x-7/5x-15=0

We calculate fractions


20x^2/30x^2+(-42x)/30x^2-15=0

We multiply all the terms by the denominator


20x^2+(-42x)-15*30x^2=0

Wy multiply elements

20x^2-450x^2+(-42x)=0

We get rid of parentheses

20x^2-450x^2-42x=0

We add all the numbers together, and all the variables

-430x^2-42x=0

a = -430; b = -42; c = 0;
Δ = b2-4ac
Δ = -422-4·(-430)·0
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-42}{2*-430}=\frac{0}{-860}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+42}{2*-430}=\frac{84}{-860}
=-21/215
$