-14X^2+4X+14=-6x^2

Solution for -14X^2+4X+14=-6x^2 equation:

-14X^2+4X+14=-6X^2

We move all terms to the left:

-14X^2+4X+14-(-6X^2)=0

We get rid of parentheses

-14X^2+6X^2+4X+14=0

We add all the numbers together, and all the variables

-8X^2+4X+14=0

a = -8; b = 4; c = +14;
Δ = b2-4ac
Δ = 42-4·(-8)·14
Δ = 464
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:

$\sqrt{\Delta}=\sqrt{464}=\sqrt{16*29}=\sqrt{16}*\sqrt{29}=4\sqrt{29}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{29}}{2*-8}=\frac{-4-4\sqrt{29}}{-16}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{29}}{2*-8}=\frac{-4+4\sqrt{29}}{-16}
$