4x2-4x-18=14+8x-2x2

Solution for 4x2-4x-18=14+8x-2x2 equation:

4x^2-4x-18=14+8x-2x^2

We move all terms to the left:

4x^2-4x-18-(14+8x-2x^2)=0

We get rid of parentheses

4x^2+2x^2-8x-4x-14-18=0

We add all the numbers together, and all the variables

6x^2-12x-32=0

a = 6; b = -12; c = -32;
Δ = b2-4ac
Δ = -122-4·6·(-32)
Δ = 912
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:

$\sqrt{\Delta}=\sqrt{912}=\sqrt{16*57}=\sqrt{16}*\sqrt{57}=4\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{57}}{2*6}=\frac{12-4\sqrt{57}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{57}}{2*6}=\frac{12+4\sqrt{57}}{12}
$