(2x-1)(x+4)=-6

Solution for (2x-1)(x+4)=-6 equation:

(2x-1)(x+4)=-6

We move all terms to the left:

(2x-1)(x+4)-(-6)=0

We add all the numbers together, and all the variables

(2x-1)(x+4)+6=0

We multiply parentheses ..

(+2x^2+8x-1x-4)+6=0

We get rid of parentheses

2x^2+8x-1x-4+6=0

We add all the numbers together, and all the variables

2x^2+7x+2=0

a = 2; b = 7; c = +2;
Δ = b2-4ac
Δ = 72-4·2·2
Δ = 33
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{-(7)-\sqrt{33}}{2*2}=\frac{-7-\sqrt{33}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{33}}{2*2}=\frac{-7+\sqrt{33}}{4}
$