X^2-14x-284=-2x

Solution for X^2-14x-284=-2x equation:

X^2-14X-284=-2X

We move all terms to the left:

X^2-14X-284-(-2X)=0

We get rid of parentheses

X^2-14X+2X-284=0

We add all the numbers together, and all the variables

X^2-12X-284=0

a = 1; b = -12; c = -284;
Δ = b2-4ac
Δ = -122-4·1·(-284)
Δ = 1280
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:

$\sqrt{\Delta}=\sqrt{1280}=\sqrt{256*5}=\sqrt{256}*\sqrt{5}=16\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-16\sqrt{5}}{2*1}=\frac{12-16\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+16\sqrt{5}}{2*1}=\frac{12+16\sqrt{5}}{2}
$