7/7x-7=7/8x-6

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

7/7x-7=7/8x-6

We move all terms to the left:

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


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 8x-6)!=0

x∈R


We get rid of parentheses

7/7x-7/8x+6-7=0

We calculate fractions


56x/56x^2+(-49x)/56x^2+6-7=0

We add all the numbers together, and all the variables

56x/56x^2+(-49x)/56x^2-1=0

We multiply all the terms by the denominator


56x+(-49x)-1*56x^2=0

Wy multiply elements

-56x^2+56x+(-49x)=0

We get rid of parentheses

-56x^2+56x-49x=0

We add all the numbers together, and all the variables

-56x^2+7x=0

a = -56; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-56)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-56}=\frac{-14}{-112}
=1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-56}=\frac{0}{-112}
=0
$