14=2x^2+4x-16

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



14=2x^2+4x-16
We move all terms to the left:
14-(2x^2+4x-16)=0
We get rid of parentheses
-2x^2-4x+16+14=0
We add all the numbers together, and all the variables
-2x^2-4x+30=0
a = -2; b = -4; c = +30;
Δ = b2-4ac
Δ = -42-4·(-2)·30
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-16}{2*-2}=\frac{-12}{-4} =+3 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+16}{2*-2}=\frac{20}{-4} =-5 $

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