(6x-7)(x-1)=28

Solution for (6x-7)(x-1)=28 equation:

(6x-7)(x-1)=28

We move all terms to the left:

(6x-7)(x-1)-(28)=0

We multiply parentheses ..

(+6x^2-6x-7x+7)-28=0

We get rid of parentheses

6x^2-6x-7x+7-28=0

We add all the numbers together, and all the variables

6x^2-13x-21=0

a = 6; b = -13; c = -21;
Δ = b2-4ac
Δ = -132-4·6·(-21)
Δ = 673
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{673}}{2*6}=\frac{13-\sqrt{673}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{673}}{2*6}=\frac{13+\sqrt{673}}{12}
$