(x-6)+(X-10)=7X/5X

Solution for (x-6)+(X-10)=7X/5X equation:

(x-6)+(x-10)=7x/5x

We move all terms to the left:

(x-6)+(x-10)-(7x/5x)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(x-6)+(x-10)-(+7x/5x)=0

We get rid of parentheses

x+x-7x/5x-6-10=0

We multiply all the terms by the denominator


x*5x+x*5x-7x-6*5x-10*5x=0

We add all the numbers together, and all the variables

-7x+x*5x+x*5x-6*5x-10*5x=0

Wy multiply elements

5x^2+5x^2-7x-30x-50x=0

We add all the numbers together, and all the variables

10x^2-87x=0

a = 10; b = -87; c = 0;
Δ = b2-4ac
Δ = -872-4·10·0
Δ = 7569
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7569}=87$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-87)-87}{2*10}=\frac{0}{20}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-87)+87}{2*10}=\frac{174}{20}
=8+7/10
$