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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

3x^2-14x-284=0

a = 3; b = -14; c = -284;
Δ = b2-4ac
Δ = -142-4·3·(-284)
Δ = 3604
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:

$\sqrt{\Delta}=\sqrt{3604}=\sqrt{4*901}=\sqrt{4}*\sqrt{901}=2\sqrt{901}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{901}}{2*3}=\frac{14-2\sqrt{901}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{901}}{2*3}=\frac{14+2\sqrt{901}}{6}
$