0=(2x+7)(x-4)

Solution for 0=(2x+7)(x-4) equation:

0=(2x+7)(x-4)

We move all terms to the left:

0-((2x+7)(x-4))=0

We add all the numbers together, and all the variables

-((2x+7)(x-4))=0

We multiply parentheses ..

-((+2x^2-8x+7x-28))=0


We calculate terms in parentheses: -((+2x^2-8x+7x-28)), so:

(+2x^2-8x+7x-28)

We get rid of parentheses

2x^2-8x+7x-28

We add all the numbers together, and all the variables

2x^2-1x-28

Back to the equation:

-(2x^2-1x-28)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-2x^2+x+28=0

a = -2; b = 1; c = +28;
Δ = b2-4ac
Δ = 12-4·(-2)·28
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-15}{2*-2}=\frac{-16}{-4}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+15}{2*-2}=\frac{14}{-4}
=-3+1/2
$