2(7x-1)(7x-1)=-3+7(7x-1)

Solution for 2(7x-1)(7x-1)=-3+7(7x-1) equation:

2(7x-1)(7x-1)=-3+7(7x-1)

We move all terms to the left:

2(7x-1)(7x-1)-(-3+7(7x-1))=0

We multiply parentheses ..

2(+49x^2-7x-7x+1)-(-3+7(7x-1))=0


We calculate terms in parentheses: -(-3+7(7x-1)), so:

-3+7(7x-1)

determiningTheFunctionDomain
7(7x-1)-3

We multiply parentheses

49x-7-3

We add all the numbers together, and all the variables

49x-10

Back to the equation:

-(49x-10)


We multiply parentheses

98x^2-14x-14x-(49x-10)+2=0

We get rid of parentheses

98x^2-14x-14x-49x+10+2=0

We add all the numbers together, and all the variables

98x^2-77x+12=0

a = 98; b = -77; c = +12;
Δ = b2-4ac
Δ = -772-4·98·12
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-77)-35}{2*98}=\frac{42}{196}
=3/14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-77)+35}{2*98}=\frac{112}{196}
=4/7
$