6x-3x^2=-14

Solution for 6x-3x^2=-14 equation:

6x-3x^2=-14

We move all terms to the left:

6x-3x^2-(-14)=0

We add all the numbers together, and all the variables

-3x^2+6x+14=0

a = -3; b = 6; c = +14;
Δ = b2-4ac
Δ = 62-4·(-3)·14
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{51}}{2*-3}=\frac{-6-2\sqrt{51}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{51}}{2*-3}=\frac{-6+2\sqrt{51}}{-6}
$