(2x-7)(4x+6)=3

Solution for (2x-7)(4x+6)=3 equation:

(2x-7)(4x+6)=3

We move all terms to the left:

(2x-7)(4x+6)-(3)=0

We multiply parentheses ..

(+8x^2+12x-28x-42)-3=0

We get rid of parentheses

8x^2+12x-28x-42-3=0

We add all the numbers together, and all the variables

8x^2-16x-45=0

a = 8; b = -16; c = -45;
Δ = b2-4ac
Δ = -162-4·8·(-45)
Δ = 1696
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:

$\sqrt{\Delta}=\sqrt{1696}=\sqrt{16*106}=\sqrt{16}*\sqrt{106}=4\sqrt{106}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{106}}{2*8}=\frac{16-4\sqrt{106}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{106}}{2*8}=\frac{16+4\sqrt{106}}{16}
$