(4x-2)(x-3)=14

Solution for (4x-2)(x-3)=14 equation:

(4x-2)(x-3)=14

We move all terms to the left:

(4x-2)(x-3)-(14)=0

We multiply parentheses ..

(+4x^2-12x-2x+6)-14=0

We get rid of parentheses

4x^2-12x-2x+6-14=0

We add all the numbers together, and all the variables

4x^2-14x-8=0

a = 4; b = -14; c = -8;
Δ = b2-4ac
Δ = -142-4·4·(-8)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-18}{2*4}=\frac{-4}{8}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+18}{2*4}=\frac{32}{8}
=4
$