(2x-7)(4x+)=112

Solution for (2x-7)(4x+)=112 equation:

(2x-7)(4x+)=112

We move all terms to the left:

(2x-7)(4x+)-(112)=0

We add all the numbers together, and all the variables

(2x-7)(+4x)-112=0

We multiply parentheses ..

(+8x^2-28x)-112=0

We get rid of parentheses

8x^2-28x-112=0

a = 8; b = -28; c = -112;
Δ = b2-4ac
Δ = -282-4·8·(-112)
Δ = 4368
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4368}=\sqrt{16*273}=\sqrt{16}*\sqrt{273}=4\sqrt{273}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{273}}{2*8}=\frac{28-4\sqrt{273}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{273}}{2*8}=\frac{28+4\sqrt{273}}{16}
$