(6x-1)(x+2)=28

Solution for (6x-1)(x+2)=28 equation:

(6x-1)(x+2)=28

We move all terms to the left:

(6x-1)(x+2)-(28)=0

We multiply parentheses ..

(+6x^2+12x-1x-2)-28=0

We get rid of parentheses

6x^2+12x-1x-2-28=0

We add all the numbers together, and all the variables

6x^2+11x-30=0

a = 6; b = 11; c = -30;
Δ = b2-4ac
Δ = 112-4·6·(-30)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-29}{2*6}=\frac{-40}{12}
=-3+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+29}{2*6}=\frac{18}{12}
=1+1/2
$