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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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


We calculate terms in parentheses: -((+x^2-1x-1x+1)), so:

(+x^2-1x-1x+1)

We get rid of parentheses

x^2-1x-1x+1

We add all the numbers together, and all the variables

x^2-2x+1

Back to the equation:

-(x^2-2x+1)


We add all the numbers together, and all the variables

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

We get rid of parentheses

-x^2+3x+2x-1+7=0

We add all the numbers together, and all the variables

-1x^2+5x+6=0

a = -1; b = 5; c = +6;
Δ = b2-4ac
Δ = 52-4·(-1)·6
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{-(5)-7}{2*-1}=\frac{-12}{-2}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+7}{2*-1}=\frac{2}{-2}
=-1
$