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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply parentheses ..

(+3x^2-1x-21x+7)+1x-7=0

We add all the numbers together, and all the variables

(+3x^2-1x-21x+7)+x-7=0

We get rid of parentheses

3x^2-1x-21x+x+7-7=0

We add all the numbers together, and all the variables

3x^2-21x=0

a = 3; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·3·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*3}=\frac{0}{6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*3}=\frac{42}{6}
=7
$