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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+2x^2-12x-1x+6)-(-2(x-6))=0


We calculate terms in parentheses: -(-2(x-6)), so:

-2(x-6)

We multiply parentheses

-2x+12

Back to the equation:

-(-2x+12)


We get rid of parentheses

2x^2-12x-1x+2x+6-12=0

We add all the numbers together, and all the variables

2x^2-11x-6=0

a = 2; b = -11; c = -6;
Δ = b2-4ac
Δ = -112-4·2·(-6)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-13}{2*2}=\frac{-2}{4}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+13}{2*2}=\frac{24}{4}
=6
$