(4x-3)(2x+1)=112

Solution for (4x-3)(2x+1)=112 equation:

(4x-3)(2x+1)=112

We move all terms to the left:

(4x-3)(2x+1)-(112)=0

We multiply parentheses ..

(+8x^2+4x-6x-3)-112=0

We get rid of parentheses

8x^2+4x-6x-3-112=0

We add all the numbers together, and all the variables

8x^2-2x-115=0

a = 8; b = -2; c = -115;
Δ = b2-4ac
Δ = -22-4·8·(-115)
Δ = 3684
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:

$\sqrt{\Delta}=\sqrt{3684}=\sqrt{4*921}=\sqrt{4}*\sqrt{921}=2\sqrt{921}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{921}}{2*8}=\frac{2-2\sqrt{921}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{921}}{2*8}=\frac{2+2\sqrt{921}}{16}
$