x(x-7)+6=2(x-1)

Solution for x(x-7)+6=2(x-1) equation:

x(x-7)+6=2(x-1)

We move all terms to the left:

x(x-7)+6-(2(x-1))=0

We multiply parentheses

x^2-7x-(2(x-1))+6=0


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

2(x-1)

We multiply parentheses

2x-2

Back to the equation:

-(2x-2)


We get rid of parentheses

x^2-7x-2x+2+6=0

We add all the numbers together, and all the variables

x^2-9x+8=0

a = 1; b = -9; c = +8;
Δ = b2-4ac
Δ = -92-4·1·8
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{-(-9)-7}{2*1}=\frac{2}{2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+7}{2*1}=\frac{16}{2}
=8
$