2x^2-4=-16x+14

Solution for 2x^2-4=-16x+14 equation:

2x^2-4=-16x+14

We move all terms to the left:

2x^2-4-(-16x+14)=0

We get rid of parentheses

2x^2+16x-14-4=0

We add all the numbers together, and all the variables

2x^2+16x-18=0

a = 2; b = 16; c = -18;
Δ = b2-4ac
Δ = 162-4·2·(-18)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-20}{2*2}=\frac{-36}{4}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+20}{2*2}=\frac{4}{4}
=1
$