X^2+14=2x^2-11

Solution for X^2+14=2x^2-11 equation:

X^2+14=2X^2-11

We move all terms to the left:

X^2+14-(2X^2-11)=0

We get rid of parentheses

X^2-2X^2+11+14=0

We add all the numbers together, and all the variables

-1X^2+25=0

a = -1; b = 0; c = +25;
Δ = b2-4ac
Δ = 02-4·(-1)·25
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10}{2*-1}=\frac{-10}{-2}
=+5
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10}{2*-1}=\frac{10}{-2}
=-5
$