2X^(2)-8x=14

Solution for 2X^(2)-8x=14 equation:

2X^(2)-8X=14

We move all terms to the left:

2X^(2)-8X-(14)=0

a = 2; b = -8; c = -14;
Δ = b2-4ac
Δ = -82-4·2·(-14)
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{11}}{2*2}=\frac{8-4\sqrt{11}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{11}}{2*2}=\frac{8+4\sqrt{11}}{4}
$