-14x2+4x+14=6x2

Solution for -14x2+4x+14=6x2 equation:

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

We move all terms to the left:

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

determiningTheFunctionDomain
-14x^2-6x^2+4x+14=0

We add all the numbers together, and all the variables

-20x^2+4x+14=0

a = -20; b = 4; c = +14;
Δ = b2-4ac
Δ = 42-4·(-20)·14
Δ = 1136
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:

$\sqrt{\Delta}=\sqrt{1136}=\sqrt{16*71}=\sqrt{16}*\sqrt{71}=4\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{71}}{2*-20}=\frac{-4-4\sqrt{71}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{71}}{2*-20}=\frac{-4+4\sqrt{71}}{-40}
$