(7(x*x)-7x)/(x-1)=0

Solution for (7(x*x)-7x)/(x-1)=0 equation:

(7(x*x)-7x)/(x-1)=0


Domain of the equation: (x-1)!=0

We move all terms containing x to the left, all other terms to the right

x!=1

x∈R


We add all the numbers together, and all the variables

(7(+x*x)-7x)/(x-1)=0

We multiply all the terms by the denominator


(7(+x*x)-7x)=0


We calculate terms in parentheses: +(7(+x*x)-7x), so:

7(+x*x)-7x

We add all the numbers together, and all the variables

-7x+7(+x*x)

We multiply parentheses

7x^2-7x

Back to the equation:

+(7x^2-7x)


We get rid of parentheses

7x^2-7x=0

a = 7; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·7·0
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*7}=\frac{0}{14}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*7}=\frac{14}{14}
=1
$