(2x-1)(x+6)=172

Solution for (2x-1)(x+6)=172 equation:

(2x-1)(x+6)=172

We move all terms to the left:

(2x-1)(x+6)-(172)=0

We multiply parentheses ..

(+2x^2+12x-1x-6)-172=0

We get rid of parentheses

2x^2+12x-1x-6-172=0

We add all the numbers together, and all the variables

2x^2+11x-178=0

a = 2; b = 11; c = -178;
Δ = b2-4ac
Δ = 112-4·2·(-178)
Δ = 1545
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{-(11)-\sqrt{1545}}{2*2}=\frac{-11-\sqrt{1545}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{1545}}{2*2}=\frac{-11+\sqrt{1545}}{4}
$